Spanish-Portuguese Relativity Meeting EREP...

Spanish-Portuguese Relativity Meeting

EREP 2017September 12th - 15th, 2017

Malaga, Spain

Conference Program

Spanish-Portuguese Relativity Meeting, 2017 Malaga, Spain

EREP 2017

Schedule at a glance (1)

The conference will be structured as follows:

• 12 Invited lectures (60 minutes including discussion). Room A.

• 72 Short talks (25 minutes including discussion). In the afternoon, three simultaneoussessions are held in rooms A, B and C.

• Poster presentations.

• A general interest talk (in Spanish) about General Relativity by the scientific bloggerFrancisco R. Villatoro. It will be held in the Rectorate building of the University ofMalaga (Paseo del Parque).

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Malaga, Spain Spanish-Portuguese Relativity Meeting, 2017

EREP 2017

Schedule at a glance (2)

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Contents

Welcome 6

Instructions for Participants 7

Invited speakers 8Krzysztof Bolejko. Gravitational entropy and the cosmological “no-hair” conjecture . 9Mihalis Dafermos. Boundedness and polynomial decay for the Teukolsky equation on

Kerr spacetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Claudia de Rham. Beyond Einstein Gravity . . . . . . . . . . . . . . . . . . . . . . . 12Alberto Enciso. Waves in asymptotically AdS backgrounds and Einstein metrics with

prescribed conformal infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Luis Lehner. Facing the challenge of testing GR, and extensions, with gravitational

waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Marc Mars. Slowly rotating stars: deriving the Hartle model from first principles . . 15Paolo Pani. Testing the nature of black holes with gravitational waves . . . . . . . . 16Istvan Racz. On the use of evolutionary methods in spaces of Euclidean signature . . 17Robert Wald. You Can’t Over-Charge or Over-Spin a Black Hole . . . . . . . . . . . . 18

General interest talk 19Francisco R. Villatoro. Agujeros negros. ¿Como ver lo invisible? . . . . . . . . . . . . 20

Contributed talks 21Luis Alberto Ake Hau. Causality and c-completion of multiwarped spacetimes . . . . 22Ana Alonso-Serrano. Entropy, entanglement and information in black hole evaporation 23Pablo Anglada. Size, angular momentum and mass for objects . . . . . . . . . . . . . 24Hans Bantilan. Non-Spherically Symmetric Collapse in Asymptotically AdS Spacetimes 25Carlos Barcelo. Probing extreme gravity in stellar collapse . . . . . . . . . . . . . . . 26Laura Bernard. Dynamics of compact binary systems in scalar-tensor theories at the

third post-Newtonian order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Irene Brito. Conformal transformations in relativistic elasticity: applications to spher-

ical symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Pablo Bueno. Entanglement equilibrium for higher order gravity . . . . . . . . . . . . 29Juan Calderon Bustillo. Searching for the full symphony of binary black holes . . . . 30Armando J. Cabrera Pacheco. Constructing higher dimensional black hole initial data

sets with prescribed boundary metric . . . . . . . . . . . . . . . . . . . . . . . . 31Pablo A. Cano. Universal black hole stability in four dimensions . . . . . . . . . . . . 32Raul Carballo-Rubio. Exact solutions for static and spherically symmetric ultra-

compact relativistic stars in semiclassical gravity . . . . . . . . . . . . . . . . . . 33Nastassja Cipriani and Jose M.M. Senovilla. Geodesic completeness in Lorentzian

warped products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Bartolome Coll, Joan J. Ferrando, and Juan A. Morales-Lladosa. Working in Rela-

tivistic Positioning Systems: the precision of location . . . . . . . . . . . . . . . 35

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I. Cordero-Carrion. On the convexity of relativistic ideal magnetohydrodynamics andthe associated gravitational wave emission . . . . . . . . . . . . . . . . . . . . . 36

Ivan P. Costa e Silva. A Hausdorff topology on the future causal boundary: yetanother rapprochement with conformal boundaries . . . . . . . . . . . . . . . . . 37

L. Filipe Costa. The gravitational “Magnus” effect . . . . . . . . . . . . . . . . . . . 38Karoly Zoltan Csukas. Notes on geometric inequalities in spherically symmetric space-

times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Roberto Dale and Diego Saez. On the CMB anisotropy deviations between AR-VTG

and GR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Roberto Emparan. The Singularity is Near . . . . . . . . . . . . . . . . . . . . . . . . 41Miguel C. Ferreira. On the motion of stars driven by scalar fields . . . . . . . . . . . 42Arthur E. Fischer. The Space of Gravitational Degrees of Freedom . . . . . . . . . . 43Ales Flandera and Martin Scholtz. Kerr-Newman Black Hole in the Formalism of

Isolated Horizons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Guillermo A. Gonzalez. The Einstein-Maxwell equations with thin layers of polarized

or magnetized matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Jonatan Herrera Fernandez. The causal boundary under the action of isometric group

actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Ondrej Hruska, Michal Karamazov, and Robert Svarc. Specific solutions to Quadratic

Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Gil Jannes. Perception tensor and Hawking versus Unruh effect near a black hole . . 49Jose Luis Jaramillo. An Ocean Drum: energetics and dynamics in a Physical Oceanography-

Gravitation dialogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Miguel Angel Javaloyes Victoria. Definitions and examples of Finsler spacetimes . . . 51Ivan Kolar. Higher-dimensional NUT-like and near-horizon geometries from the Kerr-

NUT-(A)dS metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Wojciech Kulczycki and Edward Malec. Gravitational waves in cosmological space-

times and memory effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Michele Levi. EFT of PNG with a spin & From YM theory to GR: The classical

double copy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Jorge Lopes. Chaos of the bound-states in anti-de Sitter spacetime . . . . . . . . . . . 55Hideki Maeda. Throat quantization of the Schwarzschild-Tangherlini(-AdS) black hole 56Kengo Maeda. A holographic stress-energy tensor near the Cauchy horizon inside a

rotating black hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57V.S. Manko and E. Ruiz. Energy problem in the regular black hole spacetimes . . . . 58Julija Markeviciute and Jorge E. Santos. Stirring a black hole . . . . . . . . . . . . . 59Cristian Martınez. Black hole formation with a conformally coupled scalar field in

three spacetime dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Masato Minamitsuji. Black Holes in the Generalized Proca Theory . . . . . . . . . . 61Sindy Mojica. Innermost stable circular orbits in dilatonic Einstein-Gauss-Bonnet

theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Filipe Moura. Absorption of scalars by black holes in string theory . . . . . . . . . . . 63Anna Nakonieczna. Initializing gravitational evolutions within the parabolic-hyperbolic

formulation - black holes binary . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Andrea Nerozzi. Advanced wave extraction algorithms in numerical relativity . . . . . 65Kota Ogasawara. Particle collision with an arbitrarily high center-of-mass energy near

a Banados-Teitelboim-Zanelli black hole . . . . . . . . . . . . . . . . . . . . . . 66Marcelo Ortaggio. Universal electromagnetic fields . . . . . . . . . . . . . . . . . . . . 67Tomas Ortın. Self-consistency of higher-order gravities . . . . . . . . . . . . . . . . . 68Michal Pirog. Relativistic low angular momentum accretion . . . . . . . . . . . . . . 69Alena Pravdova. On exact solutions to quadratic gravity . . . . . . . . . . . . . . . . 70

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Borja Reina. Four of a kind: I − Love−Q− δM . . . . . . . . . . . . . . . . . . . . 71Angel Rincon. Rotating BTZ black hole assuming running couplings . . . . . . . . . 72Jorge Rocha. Dynamical spacetimes in low-energy string theory and cosmic censorship 73Marcelo E. Rubio. A hyperbolic theory of relativistic conformal dissipative fluids . . . 74Diego Rubiera-Garcıa. Singular and nonsingular black holes in f(R) theories and beyond 75Nihat Sadik Deger. Homogeneous Solutions of Minimal Massive 3D Gravity . . . . . . 76Miguel Sanchez. Ehlers-Kundt conjecture about Gravitational Waves . . . . . . . . . 77Supratik Sarkar and A. Bhattacharyay. Analogue Gravity from Quantum potential in-

duced Bose-Einstein Condensates (BEC): UV-IR Coupling in analogue Hawkingradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Jose M M Senovilla. Area deficit of geodesic balls and gravitational energy . . . . . . 79C. A. S. Silva. Quantum corrected Friedmann equations from loop quantum black

holes entropy-area relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Philipp Stanzer. Quantum Null Energy Condition from Numerical Holography . . . . 81Otakar Svıtek. Wormhole models without symmetries . . . . . . . . . . . . . . . . . . 82Tayebeh Tahamtan. Spacetimes with Nonlinear Electrodynamics . . . . . . . . . . . . 83Kunihito Uzawa. Supersymmetric solution in dynamical M-brane background . . . . 84Bruno Vergara. Fractional wave operators and the wave equation in anti-de Sitter

spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Vincenzo Vitagliano. Covariantly Quantum Field Theory . . . . . . . . . . . . . . . . 86Steven Willison. Gravitational degrees of freedom and isometric embedding . . . . . . 87Helvi Witek. Black holes as probes for fundamental physics . . . . . . . . . . . . . . . 88Vojtech Witzany. New conservation laws for matter near spinning black holes . . . . . 89

Posters 90Irene Brito and Filipe Mena. Initial boundary value problem for the Einstein field

equations for a class of spherically symmetric imperfect fluids . . . . . . . . . . 91Antonino Flachi. Chiral vortical effect in curved space and the Chern-Simons current 92Apratim Ganguly. Binary boson stars and numerical relativity . . . . . . . . . . . . . 93Akio Hosoya and Shunsuke Fujii. Informational Theory of Relativity . . . . . . . . . 94F. D. Lora-Clavijo and A. Cruz-Osorio. Relativistic BHL Accretion in the Presence

of Stellar Winds and Dense Clumps Around a Black Hole . . . . . . . . . . . . . 95F. Martin-Vergara, F. Rus, and F. R. Villatoro. Pseudospherical surfaces based on

the Graphene Superlattice Equation . . . . . . . . . . . . . . . . . . . . . . . . . 96Vojtech Pravda. Universal spacetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Ignacio Sanchez-Rodrıguez. Conformal scalar invariants of weight zero . . . . . . . . . 98C.A.S.Silva and R.G.L.Aragao. Entropic corrected Newton’s law of gravitation . . . . 99

Notes 100

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EREP 2017Welcome

It is our great pleasure to welcome you to this edition of the Spanish-Portuguese RelativityMeeting, held in Malaga (Spain). These meetings are annual conferences on General Relativityand Gravitation, that date back to 1977, and are organized each year by one of the differentgroups doing research on Relativity and Gravitation in Portugal and Spain.

Scientific CommitteeNathalie Deruelle Laboratoire Astroparticule et Cosmologie

CNRS-Universite Paris7, FranceRuth Durrer Universite de Geneve, SwitzerlandValeria Ferrari Sapienza Universita di Roma, ItalyJorge Pullin Louisiana State University, USAJose M.M. Senovilla Universidad del Paıs Vasco, Spain

Organizing Committee

Miguel Atencia Departamento de Matematica Aplicada

Jose Luis Flores Departamento de Algebra, Geometrıa y Topologıa

Manuel Gutierrez Departamento de Algebra, Geometrıa y TopologıaBenjamın Olea Departamento de Matematica AplicadaFrancisco Palomo Departamento de Matematica Aplicada

Universidad de Malaga, Spain

Technical Secretariat

Viajes El Corte [email protected]

Sponsors

Universidad de Malaga http://www.uma.es

Vicerrectorado de Investigacion y TransferenciaDepartamento de Algebra, Geometrıa y TopologıaDepartamento de Matematica Aplicada

National Research Projects of the Ministerio de Economıa y Competitividad(Gobierno de Espana) and the European Union

MTM2013-47828-C2-1-PMTM2013-47828-C2-2-PMTM2016-78647-P

Academia Malaguena de Ciencias http://amciencias.com

Sociedad Malaguena de Astronomıa http://www.astromalaga.es

Metro de Malaga http://metromalaga.es

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Instructions for Participants

Internet access

• Wireless network: Congresos

– Open any web site in a browser– In the identification page that will appear, enter:

∗ Username: erep2017∗ Password: Gravitation

• Alternatively, you can use your eduroam account on the wireless network eduroam.• There are some available terminals in the computer rooms. You will have to register in

the Virtual Campus on these computers, providing your personal data.• Contact the Registration Desk or ask someone of the Organization Committee for help.

Instructions for Contributors

• Room A: Sala de grados A (2nd floor)• Room B: Sala de grados B (2nd floor)• Room C: Classroom 0.26 (ground floor)• Each room will have a digital projector and a Windows computer, but you are advised

to bring your own laptop to avoid configuration issues.• Both speakers and chairs should arrive 10 minutes before the session starts, to check the

equipment works.• Please stick to the schedule.• Posters will be displayed on A0 portrait (vertical) boards that will be installed in the hall

of the ground floor.• Contact the Registration Desk or ask someone of the Organization Committee for help.• Please, wear your badge visibly, specially at lunches.

Social program

• Date: Thursday 14th.• Meeting point for both activities: AC Hotel Malaga Palacio, Street Cortina del Muelle, 1• Walking visit to Malaga: 17:00 h.• Dinner: 20:00 h. (from the hotel we walk to the nearby restaurant).• Restaurant Los Patios de Beatas, Street Beatas, 43.• Be aware of any updates by checking the signboard next to the Registration Desk.• Please, wear your badge visibly at all social activities and lunches.

Transport

• The conference bag includes a couple of Metro tickets, each charged with two trips. Donot dispose of the cards, they can be recharged with additional trips without paying againfor the physical support (see http://metromalaga.es/en/tickets-and-fares/).

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Invited speakers

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Gravitational entropy and the cosmological “no-hair”conjecture

Krzysztof Bolejko

The University of Sydney, School of Physics, NSW 2006, [email protected]

ABSTRACT

Gravitational entropy [1] and the “no-hair” conjunctures [2, 3] are seemingly

contradictory: the growth of the first one is associated with the growth of inho-

mogeneity [4, 5, 6], while the second one argues that the dark energy dominated

Universe will asymptotically approach a homogeneous and isotropic de Sitter

state[7, 8].

In my talk I will present the analysis of both of these conjectures within the

silent universes [9, 10]. Irrotational silent universes belong to a class of systems

where each worldline evolves independently of other worldlines — there is no

communication between the worldlines, i.e. no pressure gradients, no energy

flux, no gravitational radiation. In my talk I will discuss properties and evolu-

tion of the irrotational silent universe. I will focus on the gravitational entropy

and future asymptotic state of the silent universe dominated by dark energy

[11]. Finally, I will comment on the gravitational entropy of gravitational waves.

References

[1] T. Clifton, G. F. R. Ellis, and R. Tavakol, “A gravitational entropy proposal,”Classical and Quantum Gravity, vol. 30, p. 125009, 2013.

[2] G. Gotz, “On the cosmological ’no-hair’ conjecture,” Physics Letters A,vol. 128, no. 3, pp. 129 – 132, 1988.

[3] L. G. Jensen and J. A. Stein-Schabes, “Is inflation natural?,” Phys. Rev. D,vol. 35, pp. 1146–1150, 1987.

[4] K. Bolejko and W. R. Stoeger, “Intermediate homogenization of the Uni-verse and the problem of gravitational entropy,” Phys. Rev. D, vol. 88, no. 6,p. 063529, 2013.

[5] R. A. Sussman and J. Larena, “Gravitational entropies in LTB dust models,”Classical and Quantum Gravity, vol. 31, p. 075021, 2014.

[6] R. A. Sussman , “Gravitational entropy of cosmic expansion,” AstronomischeNachrichten, vol. 335, p. 587, 2014.

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[7] R. M. Wald, “Asymptotic behavior of homogeneous cosmological models inthe presence of a positive cosmological constant,” Phys. Rev. D, vol. 28,pp. 2118–2120, 1983.

[8] T. Pacher and J. A. Stein-Schabes, “On the Locality of the No Hair Con-jecture and the Measure of the Universe,” Annalen der Physik, vol. 503,pp. 518–526, 1991.

[9] M. Bruni, S. Matarrese, and O. Pantano, “Dynamics of silent universes,”Astroph. J., vol. 445, pp. 958–977, 1995.

[10] H. van Elst, C. Uggla, W. M. Lesame, G. F. R. Ellis, and R. Maartens, “Inte-grability of irrotational silent cosmological models,” Classical and QuantumGravity, vol. 14, pp. 1151–1162, 1997.

[11] K. Bolejko, In preparation, 2017.

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Boundedness and polynomial decay for the Teukolskyequation on Kerr spacetimes

Mihalis Dafermos

University of Cambridge, Department of Pure Mathematics and MathematicalStatistics, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

: [email protected]

ABSTRACT

This is joint work with Igor Rodnianski and Gustav Holzegel. As part of our

previous proof of linear stability of Schwarzschild, we showed both boundedness

and polynomial decay estimates for solutions of the spin ±2 Teukolsky equation

by exploiting a physical space transformation to solutions of the Regge-Wheeler

equation. We show how this procedure generalises to yield similar results for

the Teukolsky equation on Kerr.

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Beyond Einstein Gravity

Claudia de Rham

Theoretical Physics, Blackett Laboratory, Imperial College, London, [email protected]

ABSTRACT

One hundred years after ”Die Feldgleichungen der Gravitation” by Albert

Einstein and at the beginning of a new era of direct gravitational detections,

the time is right to pause and ponder about the nature of the particle carrier

of the gravitational force: the graviton. To unify the theory of gravity with the

other forces of nature we expect the theory of General Relativity to be modified

at small distances. Could it be that General Relativity is also modified at large

distances as large as our current observable Universe? This may depend on the

very nature of the graviton.

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Waves in asymptotically AdS backgrounds and Einsteinmetrics with prescribed conformal infinity

Alberto Enciso

Instituto de Ciencias Matematicas, Consejo Superior de InvestigacionesCientıficas, 28049 Madrid, SPAIN

[email protected]

ABSTRACT

In this talk we will consider a couple of mathematical problems about wave

propagation in asymptotically AdS spaces. In particular, we will discuss a suit-

able local wellposedness theorem for the Einstein equations that ensures the

existence of Einstein metrics with prescribed conformal geometry. The talk is

based on joint work with Niky Kamran and Bruno Vergara.

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Facing the challenge of testing GR, and extensions, withgravitational waves

Luis Lehner

Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, CanadaCIFAR, Cosmology and Gravity Program, Toronto, ON M5G 1Z8, Canada

[email protected]

ABSTRACT

Exploiting gravitational waves to probe the underlying gravitational theory

requires a thorough understanding of possible surprises in GR, as well as possible

departures from it. In this talk i will discuss a few interrelated challenges in

this task and ways to address them.

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Slowly rotating stars: deriving the Hartle model from firstprinciples.

Marc Mars

Instituto de Fısica Fundamental y Matematicas, Universidad de Salamanca,Plaza de la Merced s/n, 37008 Salamanca, Spain

[email protected]

ABSTRACT

The Hartle model describes slowly rigidly rotating stars in the strong field

regime by using perturbation theory up to second order. The model involves

a number of hypotheses, particularly regarding the structure of the fields when

expanded in spherical harmonics that need justification. In this talk I present

work in collaboration with Reina and Vera where the Hartle model is derived

from first principles. Our results prove in particular that, at this level of approx-

imation, the spacetime must be equatorially symmetric and is fully determined

by two parameters, namely the central pressure and the rotation parameter of

the fluid.

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Testing the nature of black holes with gravitational waves

Paolo Pani

CENTRA, Departamento de Fısica, Instituto Superior Tecnico, Universidade deLisboa, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal

Dipartimento di Fisica, “Sapienza” Universita di Roma and Sezione INFNRoma1, Piazzale Aldo Moro 5, 00185, Roma, Italy

[email protected]

ABSTRACT

Gravitational wave (GW) astronomy allows us for unprecedented tests of the

nature of dark compact objects. In this context, I will discuss two signatures

of new physics at the horizon scale: GW “echoes” in the postmerger ringdown

phase of a binary coalescence, and finite-size effects of exotic compact objects

that affect the inspiral premerger phase. In the first case, the ringdown wave-

form of exotic ultracompact objects is initially identical to that of a black hole,

and putative corrections at the horizon scale appear only at later times as a mod-

ulated and distorted train of echoes of the modes of vibration associated with the

photon sphere. As for the second case, I will discuss the tidal heating and tidal

Love numbers of different families of boson stars, gravastars, wormholes, and

other toy models for quantum corrections at the horizon scale. These corrections

display a universal logarithmic dependence on the location of the surface in the

black-hole limit. I will discuss the ability of present and future GW detectors to

measure these effects. Both LIGO, ET and LISA can impose interesting con-

straints on boson stars, while LISA is able to probe even Planckian corrections.

We argue that these effects provide a smoking gun of new physics at the horizon

scale, and that future GW measurements of a binary coalescence provide a novel

way to test black holes and general relativity in the strong-field regime.

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On the use of evolutionary methods in spaces of Euclideansignature

Istvan Racz

Wigner RCP, Konkoly Thege Miklos ut 29-33, H-1121 Budapest, [email protected]

ABSTRACT

Two examples of physical interest will be presented. Both, contrary to the

folklore, demonstrate that evolutionary methods may play a significant role in

spaces of Euclidean signature. First, the propagation of the constraints is con-

sidered. It is shown that once a clear separation of the evolutionary and con-

straint equations is done, the subsidiary equations satisfied by the constraint

expressions form a first order symmetric hyperbolic system regardless whether

the ambient Einsteinian space is of Lorentzian or Euclidean signature. Second,

the constrains of Einstein’s theory of gravity are considered. Since the seminal

observations of Lichnerowicz and York these equations are usually referred to

as a semilinear elliptic system. It will be shown that-according to the choice of

the dependent variables-the constraints may have different characters. In par-

ticular, they may take the form of either a parabolic-hyperbolic or a strongly

hyperbolic system. Some of the recent developments related to these alternative

forms will also be discussed..

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17


You Can’t Over-Charge or Over-Spin a Black Hole

Robert Wald

Enrico Fermi Institute and Department of Physics, The University of Chicago,5640 South Ellis Avenue, Chicago, Illinois 60637, USA

[email protected]

ABSTRACT

The Kerr-Newman solutions are the only stationary black hole solutions of the

Einstein-Maxwell equations in 4-dimensions. However, these solutions describe

black holes only when the inequality M2 ≥ (J/M)2 + Q2 is satisfied, where

M , J , and Q are the mass, angular momentum, and charge of the black hole.

Therefore, if an extremal or nearly extremal black hole can be made to absorb

matter with sufficiently large angular momentum or charge as compared with

its energy, one would obtain an apparent contradiction with cosmic censorship.

Hubeny and others have made proposals as to how this might be done, but a

proper analysis of this proposal requires a calculation of all second order effects

on energy, including, in particular, effects arising from self-force. We show in

this work that when all of the second order effects are taken into account, no

over-charging or over-spinning of a black hole can occur, provided only that the

non-electromagnetic matter satisfies the null energy condition.

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General interest talk

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Agujeros negros. ¿Como ver lo imposible?

Francisco R. Villatoro

Universidad de [email protected]

ABSTRACT

Se espera que este verano (quizas antes de septiembre) se publique la primera

observacion del agujero negro supermasivo de nuestra galaxia con una resolucion

comparable al tamano de su horizonte de sucesos (algo ası como la orbita de

Mercurio). Hasta ahora solo se ha observado con una distancia del orden de la

orbita de Neptuno.

Las observaciones se estan realizando ahora mismo y ya son noticia en algunos

medios: se esta usando una red de telescopios a escala mundial que equivalen a

un telescopio con un espejo del tamano de toda la Tierra. Tanto si para el dıa de

la charla ya se han publicado estos resultados, como si aun no se han publicado,

creo que en septiembre esta noticia aparecera en varios medios. Por ello sobre

esa fecha el publico estara muy interesado en los agujeros negros supermasivos

y como se ven usando redes de telescopios.

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Contributed talks

21


Causality and c-completion of multiwarped spacetimes

Luis Alberto Ake Hau.

Universidad de Malaga, Departamento de Algebra, Geometrıa y Topologı[email protected]

ABSTRACT

We discuss the causal properties of doubly warped spacetimes and the causal

boundary of these spacetimes. Some applications of our results in examples of

physical interest are considered: Schwarzschild spacetimes, Reissner Nordstrom

and in the context of Maldacena’s conjecture. This talk is based on the joint

work with J.L. Flores and J. Herrera in [1].

References

[1] L. Ake, J.L. Flores and J. Herrera, Causality and c-completion of doublywarped spacetimes, arXiv:1709.00234.

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22


Entropy, entanglement and information in black holeevaporation

Ana Alonso-Serrano

Institute of Theoretical Physics, Faculty of Mathematics and Physics, CharlesUniversity, 18000 Prague, Czech Republic

[email protected]

ABSTRACT

It can be found that blackbody radiation contains (on average) an entropy

of 3.9± 2.5 bits per photon. The flip side of this observation is the information

budget: If the emission process is unitary, as it certainly is for normal physical

burning, then this entropy is exactly compensated by the “hidden information”

in the correlations that we choose not to consider within the specific coarse-

graining. We can also extend this argument to the Hawking radiation from

black holes, demonstrating that the assumption of unitarity leads to a perfectly

reasonable entropy/information budget.

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Size, angular momentum and mass for objects

Pablo Anglada

Facultad de Matematica, Astronomıa y Fısica, Universidad Nacional de Cordoba,Instituto de Fısica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria,

Cordoba, [email protected]

ABSTRACT

We present a new geometrical inequality involving the ADM mass, the angu-

lar momentum and the size of an ordinary axially symmetric object. The main

tool we use to use to prove it is the monotonicity of the Geroch quasi- local

energy along the inverse mean curvature flow. We also compute numerical

examples to test the robustness of our hypotheses and results. [1].

References

[1] Anglada, Pablo and Gabach-Clement, M. E. and Ortiz, Omar E. Size, angularmomentum and mass for objects. arXiv [gr-qc], 1612.08658, 2016.

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24


Non-Spherically Symmetric Collapse in Asymptotically AdSSpacetimes

Hans Bantilan

School of Mathematical Sciences, Queen Mary University of London, Mile EndRoad, London E1 4NS, United Kingdom

Centre for Research in String Theory, School of Physics and Astronomy, QueenMary University of London, E1 4NS, UK

Department of Applied Mathematics and Theoretical Physics (DAMTP), Centrefor Mathematical Sciences, University of Cambridge, Wilberforce Road,

Cambridge CB3 0WA, United [email protected]

ABSTRACT

We numerically simulate gravitational collapse in asymptotically anti-de Sit-

ter spacetimes away from spherical symmetry. Starting from initial data sourced

by a massless real scalar field, we solve the Einstein equations with a negative

cosmological constant in five spacetime dimensions and obtain a family of non-

spherically symmetric solutions, including those that form two distinct black

holes on the axis. We find that these configurations collapse faster than spheri-

cally symmetric ones of the same mass and radial compactness. Similarly, they

require less mass to collapse within a fixed time.

1

25


Probing extreme gravity in stellar collapse

Carlos Barcelo

Instituto de Astrofısica de Andalucıa IAA-CSIC, Glorieta de la Astronomıa s/n,18008 Granada, Spain

[email protected]

ABSTRACT

The standard way to understand quantum corrected black holes leads to the

information loss paradox and the lifetime dilemma. A radical way out of this

situation is to give up a hypothesis which is tacitly assumed in the vast majority

of works on the subject: that the classical singularity is substituted by something

effectively acting as a sink for a long period of time, as seen by asymptotic ob-

servers. Eliminating this characteristic changes drastically much of the physics

now associated to black holes. A nice feature of the new hypothesis it that it of-

fers a clear possibility of experimental falsifiability with upcoming gravitational

waves observations. In this talk I will discuss these possibilities.

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26


Dynamics of compact binary systems in scalar-tensortheories at the third post-Newtonian order

Laura BERNARD

Instituto Superior Tecnico - [email protected]

ABSTRACT

In the upcoming years, the observation of gravitational waves from inspiraling

compact binary systems will allow us to test General Relativity in its strong

field regime. Both the detection and precise determination of the physical

parameters of gravitational waves require a bank of very accurate template

gravitational waveforms. In order to constrain the deviations from General

Relativity, one also has to build template waveforms in alternative theories of

gravity. In this talk, I will focus on massless scalar-tensor theories and address

the question of the dynamics of non-spinning compact binary systems at 3PN

order in harmonic coordinates. This is needed in order to compute the scalar

and gravitational waveforms at 2PN order. In particular, I will present our

method which is based on a Fokker action adapted to the specificities of both

the post-Newtonian formalism and ST theories. I will then derive the conserved

energy and momentum at 3PN order.

1

27


Conformal transformations in relativistic elasticity:applications to spherical symmetry

Irene Brito

Centro de Matematica, Universidade do Minho, 4710-057 Braga, [email protected]

ABSTRACT

Conformal space-time configurations are considered in the context of gen-

eral relativistic elasticity. Expressions relating densities, pressures and energy-

momentum tensors are obtained for the conformal configurations. The results

are applied to spherically symmetric space-times with elastic matter [1],[2],

showing how a new non-static shear-free solution of the Einstein field equations

can be generated [3].

References

[1] Brito, I., Carot, J., Vaz, E.G.L.R., Gen. Rel. Grav. 42, 2357 (2010) and Gen.Rel. Grav. 44, 287 (2012).

[2] Magli, G., Gen. Rel. Grav. 24, 139 (1992).

[3] Brito, I., J. Math. Phys 56, 092502 (2015).

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28


Entanglement equilibrium for higher order gravity

Pablo Bueno

Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001Leuven, Belgium

[email protected]

ABSTRACT

I will start with a quick review of the main approaches to the problem of

deriving gravitational dynamics from entanglement/thermodynamic-based prin-

ciples. My focus will be then on Jacobson’s recent “entanglement equilibrium”

proposal [1], which connects Einstein’s equations to an equilibrium condition

on the entanglement entropy of small spherical regions in vacuum. I will ex-

plain that this principle can be extended to the linearized equations of general

higher-derivative corrections [2]. These corrections are naturally associated with

the subleading divergences in the entanglement entropy, which take the form of

a Wald entropy evaluated on the entangling surface. Variations of this Wald

entropy are related to the field equations through a new identity for causal dia-

monds in maximally symmetric spacetimes. If the variations are taken holding

fixed a geometric functional that we called the “generalized volume”, the identity

becomes an equivalence between the linearized constraints and the entanglement

equilibrium condition. I will explain that the fully nonlinear higher curvature

equations cannot be derived from the linearized equations applied to small balls,

in contrast to the situation encountered in Einstein gravity. I will also discuss

possible applications of our generalized volume (which generalizes the notion of

volume to higher-derivative gravities in a similar way as Wald’s entropy func-

tional generalizes that of area), e.g., in the context of holographic complexity.

References

[1] T. Jacobson, Phys. Rev. Lett. 116 (2016) no.20, 201101 [arXiv:1505.04753[gr-qc]].

[2] P. Bueno, V. S. Min, A. J. Speranza and M. R. Visser, Phys. Rev. D 95(2017) no.4, 046003 [arXiv:1612.04374 [hep-th]].

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29


Searching for the full symphony of binary black holes

Juan Calderon Bustillo

Center for Relativistic Astrophysics and School of Physics, Georgia Institute ofTechnology, Atlanta, GA 30332

[email protected]

ABSTRACT

The discovery of the gravitational wave signals GW150914 and GW151226

has open the era of gravitational wave astronomy [1, 2]. The source of both sig-

nals were identified as binary black holes with mass ratio q < 3 and a total mass

below 100M�. Furthermore, a search for heavier systems recently reported no

detections [3]. Current searches for binary black holes omit the so called higher

order modes, focusing only on the identification of the dominant mode of the

emitted gravitational waves. In this talk I will present a search for binary black

holes that considers all the modes of the emitted radiation. This is crucial in

order to detect more exotic sources than the ones LIGO has currently detected:

large mass ratio and intermediate mass binary black holes [4].

References

[1] B. P. Abbott et al. (Virgo, LIGO Scientific), Phys. Rev. Lett. 116, 061102(2016), arXiv:1602.03837 [gr-qc].

[2] B. Abbott et al. (Virgo, LIGO Scientific), Phys. Rev. Lett. 116, 241103 (2016),arXiv:1606.04855 [gr-qc].

[3] B. P. Abbott et al. (Virgo, LIGO Scientific), (2017), arXiv:1704.04628 [gr-qc].

[4] Juan Calderon Bustillo, Pablo Laguna, and Deirdre Shoemaker Phys. Rev. D95, 104038

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30


Constructing higher dimensional black hole initial data setswith prescribed boundary metric

Armando J. Cabrera Pacheco

Mathematics Department, University of [email protected]

ABSTRACT

Recently Mantoulidis and Schoen [1] constructed smooth asymptotically flat

initial data sets with prescribed horizon boundary, whose mass can be made ar-

bitrarily close to the optimal value in the Riemannian Penrose inequality, while

the geometry of the horizon is far from being rotationally symmetric. In this

talk, combining their construction with some geometric flows, we will discuss

how to obtain higher dimensional initial data sets with analogous properties.

This talk is based on a joint work with Pengzi Miao [2].

References

[1] Mantoulidis, C.; Schoen, R., On the Bartnik mass of apparent horizons, Class.Quantum Grav., 32 (2015), no. 20, 205002, 16pp.

[2] Cabrera Pacheco, A. J.; Miao, P., Higher dimensional black hole initial datawith prescribed boundary metric, arXiv:1505.01800.

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31


Universal black hole stability in four dimensions

Pablo A. Cano

Instituto de Fısica Teorica UAM/CSIC, C/ Nicolas Cabrera, 13-15,C.U. Cantoblanco, 28049 Madrid, Spain

[email protected]

ABSTRACT

We show that four-dimensional black holes become stable below certain mass

when the Einstein- Hilbert action is supplemented with higher-curvature terms.

We prove this to be the case for an infinite family of ghost-free theories involv-

ing terms of arbitrarily high order in curvature. The new black holes, which

are non-hairy generalizations of Schwarzschild’s solution, present a universal

thermodynamic behavior for general values of the higher-order couplings. In

particular, small black holes have infinite lifetimes. When the evaporation pro-

cess makes the semiclassical approximation break down (something that occurs

after a time which is usually infinite for all practical purposes), the resulting

object retains a huge entropy, in stark contrast with Schwarzschild’s case.

References

[1] P. Bueno and P. A. Cano, “Universal black hole stability in four dimensions”,arXiv:1704.02967 [hep-th].

1

32


Exact solutions for static and spherically symmetricultra-compact relativistic stars in semiclassical gravity

Raul Carballo-Rubio

SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di [email protected]

ABSTRACT

Astrophysical black holes may be ultra-compact relativistic stars instead of

proper general-relativistic black holes. The detection of gravitational waves has

revived interest in this possibility, that has been under development by a few

different groups during the last decade. The theoretical status of these hypo-

thetical objects is however uncertain. In this talk I will present some recent

developments aimed at changing this situation. In particular, I will discuss:

(i) how to construct an extension of the equations of stellar equilibrium in gen-

eral relativity to include the semiclassical effect of quantum vacuum polarization,

and (ii) that there exist exact solutions to these equations, describing static and

spherically symmetric ultra-compact relativistic stars. This talk will be based on

[1].

References

[1] Raul Carballo-Rubio, “Stellar equilibrium in semiclassical gravity”arXiv:1706.05379 (2017).

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33


Geodesic completeness in Lorentzian warped products

Nastassja Cipriani and Jose M. M. Senovilla

KU Leuven, Department of Mathematics, Celestijnenlaan 200B – Box 2400,BE-3001 Leuven, Belgium

Fısica Teorica, Universidad del Paıs Vasco, Apartado 644, 48080 Bilbao, [email protected]

ABSTRACT

Most singularity theorems in general relativity are based on the existence of

trapped submanifolds with co-dimension two. In [1] the authors show that this

can be generalized: they prove singularity theorems by using trapped submani-

folds with arbitrary co-dimension. In particular, they provide a key, sufficient,

trapping condition (*) for the existence of focal points.

Let M be a Lorentzian manifold of dimension 4, Y a compact Riemannian man-

ifold of dimension 6, and consider the warped product M = M ×f Y. We make

a systematic study of the spacelike submanifolds ofM and, using condition (*),

find those admitting focal points. When possible, we show that M is geodesi-

cally incomplete, thus singular. Our results have applications to the instability

of extra space dimensions in string theory [2].

References

[1] G.J.Galloway and J.M.M.Senovilla, “Singularity theorems based on trappedsubmanifolds of arbitrary co-dimension”, Classical Quant. Grav. 27 (2010),no. 15, 152002, 10 pp

[2] R. Penrose, “On the instability of extra space dimensions” in The futureof the theoretical physics and cosmology, G. W. Gibbons, E. P. S. Shellard,and S. J. Rankin, eds. (Cambridge, 2002), 185–201, Cambridge Univ. Press,Cambridge, 2003

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34


Working in Relativistic Positioning Systems: the precisionof location

Bartolome Coll, Joan J. Ferrando and Juan A. Morales–Lladosa

Universitat de Valencia, Departament d’Astronomia i Astrofı[email protected], [email protected], [email protected]

ABSTRACT

Relativistic Positioning Systems (RPSs) are the sole known locating systems

allowing to construct, in any space-time, primary physical coordinate systems.

The fundamental concepts of the theory of RPSs are already known, but its

implementation needs further development ([1-5]). The basic ingredient of the

theory is a set of four emitters broadcasting their proper times (emission coor-

dinates). In this talk, the main RPSs topics are presented. In particular, for a

basic RPS in a flat space-time, we are interested in the precision with which it

is able to locate space-time events. It appears that this precision is related to

the Jacobian, J , of the transformation from emission to inertial coordinates.

We stress in detail how the value of J is related to the uncertainties in the de-

termination of the position at every event. This result is interesting in current

navigation satellite systems. For instance, among the visible satellite tetrads

for a user, that which provides the more precise user position is the one having

the maximum value of J .

References

[1] B. Coll, Relativistic positioning systems: perspectives and prospects, ActaFutura, 7, 35-47 (2013).

[2] B. Coll, J. J. Ferrando and J. A. Morales-Lladosa, Positioning systems inMinkowski spacetime: from emission to inertial coordinates, Class. QuantumGrav. 27, 065013 (2010).

[3] B. Coll and J. M. Pozo, Relativistic positioning systems: the emission coor-dinates, Class. Quantum Grav. 23, 7395-7416 (2006).

[4] P. Delva, U. Kostic, and A. Cadez, Numerical modeling of a Global Naviga-tion Satellite System in a general relativistic framework, Advances in SpacesResearch, 47, 370-379 (2011).

[5] N. Puchades and D. Saez, Approaches to relativistic positioning around Earthand error estimations, Advances in Spaces Research, 57, 499-508 (2016).

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35


On the convexity of relativistic idealmagnetohydrodynamics and the associated gravitational

wave emission

I. Cordero-Carrion

University of Valencia, C/ Dr. Moliner 50, 46100 Burjassot, Valencia (Spain)[email protected]

ABSTRACT

This work has been done in collaboration with J. M. Ibanez, N. Sanchis-

Gual, J.A. Font, M.A. Aloy, J.M. Martı, J.A. Miralles and A. Marquina. We

analyze the influence of the relativistic effects and magnetic field in the con-

vexity properties of the relativistic magnetohydrodynamics system of equations.

To this purpose we use the approach of Lax, based on the analysis of the lin-

early degenerate / genuinely nonlinear nature of the characteristic fields. The

non-relativistic, unmagnetized limits are properly recovered. The characteristic

fields corresponding to the material and Alfven waves are linearly degenerate

and, then, not affected by the convexity issue. The analysis of the characteris-

tic fields associated with the magnetosonic waves reveals, however, a dependence

of the convexity condition on the magnetic field. The result is expressed in the

form of a generalized fundamental derivative written as the sum of two terms

[1]. The first one is the generalized fundamental derivative in the case of purely

hydrodynamical (relativistic) flow [2]. The second one contains the effects of

the magnetic field, and generalizes the non-relativistic magnetic case [3]. To

illustrate the influence of the relativistic effects encoded in the first term, we

present some numerical simulations using an EoS for which the sound speed is

non-monotonous, which implies that the fundamental derivative can be negative

and the EoS non-convex. Non-convex fluid dynamics can yield to the devel-

opment of unusual wave structures such as rarefaction-shocks and compound

waves. We use a non-convex phenomenological EoS to evolve a rotating star as

a toy model and compute the gravitational wave emission.

References

[1] J.M. Ibanez, I. Cordero-Carrion, M.A. Aloy, J.M. Martı and J.A. Miralles.Class. Quantum Grav. 32, 095007 (2015).

[2] J.M. Ibanez, I. Cordero-Carrion, J.M. Martı and J.A. Miralles. Class. Quan-tum Grav. 30, 057002 (2013).

[3] S. Serna and A. Marquina. Phys. Fluids 26, 016101 (2014).

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36


A Hausdorff topology on the future causal boundary: yetanother rapprochement with conformal boundaries

Ivan P. Costa e Silva

Department of Mathematics, Federal University of Santa [email protected]

ABSTRACT

A natural Hausdorff topology τc is defined on the future causal completion M

of a spacetime M with the following desirable features: the chronological future

and pasts of points in M are open, future-directed sequences converge, M is a

open dense set in M and the inclusion i : M → M is open and continuous. In

particular, the induced topology in M coincides with the manifold topology. The

topology τc is shown to be strictly finer than the future chronological topology

introduced in [1] and extensively discussed and championed in [2]. Inspired by

recent work of O. Muller [3], this topology is compared to the future conformal

boundary of M induced by a conformal extension M ↪→ M such that (i) M is a

globally hyperbolic spacetime, (ii) M ⊂ I−(K, M) for some compact set K ⊂ Mand (iii) M is causally convex in M . Of course, the standard conformal exten-

sions of Minkowski, Schwarzschild and Robertson-Walker spacetimes are of this

sort. Although τc is a priori distinct from the (also Hausdorff) topology defined

on the future causal completion in [3], it reproduces results obtained therein for

the future conformal boundary ∂+M := I+(M, M)∩∂M , namely (a) that ∂+M

is a C0 achronal hypersurface in M homeomorphic to a Cauchy hypersurface

in M , and (b) M ∪ ∂+M endowed with the topology induced by its inclusion in

M is homeomorphic to M with the topology τc. The homeomorphism maps the

conformal boundary onto the future causal boundary, so that both boundaries

coincide and are homeomorphic to Cauchy hypersurfaces in M .

References

[1] J.L. Flores, The Causal Boundary of spacetimes revisited, Commun. Math.Phys. 276 (2007), 611-643.

[2] J.L. Flores, J. Herrera and M. Sanchez, On the final definition of the causalboundary and its relation with the conformal boundary, Adv. Theor. Math.Phys. Volume 15 (2011), 991-1058. arXiv:1001.3270

[3] O. Muller, Which spacetimes admit conformal compactifications?, to appearin Adv. Theor. Math. Physics (2017), arXiv:1409.8136.

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37


The gravitational “Magnus” effect

L. Filipe Costa

Center for Mathematical Analysis, Geometry and Dynamical Systems(CAMGSD), Instituto Superior Tecnico, Universidade de Lisboa, Portugal

[email protected]

ABSTRACT

It is well known that a spinning body moving in a fluid suffers a force orthog-

onal to its velocity and rotation axis — it is called the Magnus effect. Recent

(indirect) theoretical predictions [1] and numerical simulations [2], inferred from

the effect of a spinning back hole on the surrounding matter, have suggested that

a somewhat analogous effect may take place in gravity, although its magnitude

and precise direction were still unclear. Starting from the rigorous equations of

motion for spinning bodies in General Relativity (Mathisson-Papapetrou-Dixon

equations), we show that indeed such an effect takes place, it is a fundamental

part of the spin-curvature force, and arises whenever, relative to the body, a

current of mass/energy, non-parallel to its spin, exists. We compute it in some

astrophysical systems of interest: a galactic dark matter halo, a black hole ac-

cretion disk, and FLWR spacetime. We consider also the reciprocal problem:

the “force” exerted by the body on the surrounding matter, showing that (from

this perspective) the effect is due to the body’s gravitomagnetic field. In the

process we clarify some common misconceptions regarding the action-reaction

law in post-Newtonian gravity.

References

[1] H. Okawa, V. Cardoso, Phys. Rev. D 90, 104040 (2014).

[2] J. A. Font, J. M. Ibanez, P. Papadopoulos, MNRAS 305, 920 (1999).

[3] L. F. O. Costa, R. Franco, V. Cardoso, to appear.

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38


Notes on geometric inequalities in spherically symmetricspacetimes

Karoly Zoltan Csukas

Wigner Research Center for Physics, [email protected]

ABSTRACT

ADM mass is usually preferred against quasi-local notions of mass in de-

riving geometric inequalities. In spherical symmetry there is a highly accepted

quasi-local notion of mass: the Misner-Sharp mass. It is closely related to the

energy contained within a 2-surface and its null-expansions, which are used to

determine if a surface is trapped. My talk is to present some cases where the

use of the Misner-Sharp mass is rewarding.

39


On the CMB anisotropy deviations between AR-VTG andGR.

Roberto Dale1 and Diego Saez2,3

1Departament d’Estadıstica, Matematiques i Informatica, Universitat MiguelHernandez, 03202-Elx, Alacant, Spain.

[email protected] de Astronomıa y Astrofısica, Universidad de Valencia,

46100-Burjassot, Valencia, Spain.3Observatorio Astronomico, Universidad de Valencia, E-46980 Paterna,

Valencia, [email protected]

ABSTRACT

As is well known, Cosmic Microwave Background (CMB) anisotropies are

divided into two types: those produced at decoupling and before (primary

anisotropies), and the anisotropies generated between the last scattering surface

and the observer (secondary). There is a viable vector-tensor gravity (VTG)

theory, whose vector field produces repulsive forces, and those corresponding

to the cosmological background are identical to the forces produced by vacuum

energy (cosmological constant) [1, 2, 3]. VTG has been also studied in static

spherically symmetric case, in which the existence and number of event horizons

have been proved to be dependent on the value of a certain VTG parameter [4].

There exists opposite gravitational forces in this theory, so it will be hereafter

called AR-VTG (attractive-repulsive vector-tensor gravity). In this paper we

study some differences between the cosmological predictions of AR-VTG and

those of the standard model of general relativity (GR) with cold dark matter

and cosmological constant. In particular, we show that the differences between

the CMB anisotropies of both models are secondary, since they are due to the

so-called late integrated Sachs Wolfe effect.

References

[1] R. Dale, J.A. Morales and D. Saez, arXiv:0906.2085[astro-ph.CO]

[2] R. Dale and D. Saez, Phys. Rev. D, 89, 044035 (2014)

[3] R. Dale and D. Saez, J. Cosmol. Astropart. Phys, 01 (2017) 004

[4] R. Dale, M.J. Fullana and D. Saez, Astrophys. Space Sci. 357, 116 (2015)

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40


The Singularity is Near

Roberto Emparan

ICREA and Universitat de [email protected]

ABSTRACT

I discuss work with Umpei Miyamoto and Jorge Rocha to understand the

violation of cosmic censorship in the evolution and break up of black strings,

using ideas borrowed from the theory of drop formation in fluid jets.

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41


On the motion of stars driven by scalar fields

Miguel C. Ferreira

CENTRA, Departamento de Fısica, Instituto Superior Tecnico, Universidade deLisboa,

Avenida Rovisco Pais, 1, 1049 Lisboa, [email protected]

ABSTRACT

Ultra light scalar fields have been predicted in a variety of scenarios and advo-

cated as a possible component of dark matter [1]. Its phenomenology includes the

formation of compact regular structures - boson stars [2] - and, in the presence

of a black hole, of scalar hair [3, 4]. In the latter case, the scalar field modifies

the geometry of the spacetime surrounding the black hole, which gives rise to

non-trivial effects on the motion of bodies orbiting it. We address this question

by analysing an Extreme Mass Ratio Inspiral composed of a super massive black

hole supporting an ultra light scalar field, which is orbited by a compact object

(a stellar mass black hole, a neutron star or a white dwarf). Given the fact

that the mass of the scalar field is very small, we use a perturbative approach

to investigate its contribution to the motion of the compact object. We find

that the presence of the scalar field leaves imprints on the orbital motion of the

compact object, particularly it is responsible for the appearance of resonant or-

bits whose location depend on its mass. The existence of these resonances may

enable angular momentum exchange between the scalar field and the orbiting

object, giving rise to mechanisms similar to planet migration in proto-planetary

discs. These effects have a direct consequence on the orbital evolution of binary

systems and may be used as probes for the existence of scalar fields.

References

[1] L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Phys. Rev. D95, 043541(2017), arXiv:1610.08297 [astro-ph.CO]

[2] S. L. Liebling and C. Palenzuela, Living Rev. Rel. 15, 6 (2012),arXiv:1202.5809 [gr-qc]

[3] H. Okawa, H. Witek, and V. Cardoso, Phys. Rev. D89, 104032 (2014),arXiv:1401.1548 [gr-qc]

[4] C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014),arXiv:1403.2757 [gr-qc]

1

42


The Space of Gravitational Degrees of Freedom

Arthur E. Fischer

Department of Mathematics, University of California, Santa Cruz, CA [email protected]

ABSTRACT

In general relativity, physical states are represented by isometry classesof solutions of Einstein’s field equations. The resulting space Grav(V ) ofthe totality of such states on a 4-dimensional manifold V is known as thespace of gravitational degrees of freedom. We investigate the mathematicalstructure of this space when V is di↵eomorphic to R ⇥ M , where M is aclosed 3-dimensional manifold which represents the spatial cosmic topologyof the universe. One of our main results is how the topology of M getsencoded into the structure of Grav(V ). We give a simple generic topologi-cal condition on M such that for spacetimes with constant mean curvaturehypersurfaces, Grav(V ) has the natural structure of an infinite-dimensionalsymplectic manifold on an open dense subset and that on the complementof this set, a nowhere dense subset, Grav(V ) has singularities which are oforbifold type, that is, of a manifold modulo a finite group action.

Let ⌧ be a real number < 0 and let E⌧ (V ) denote the space of globally-hyperbolic maximally-developed vacuum spacetimes that admit a Cauchy hy-persurface ⌃⌧ with (CMC) constant mean curvature = ⌧. Let D(V ) denotethe group of di↵eomorphisms of V . The space of gravitational degrees offreedom of E⌧ (V ) is then defined to be Grav⌧ (V ) = E⌧ (V )/D(V ). LetCH(M)\C�(M)\C⌧ (M) denote the intersection of the spaces of ADM Cauchydata (g, ⇡) on M that satisfy the Hamiltonian and divergence constraints andthat have constant mean curvature ⌧ . Then we construct a natural bijection

Grav⌧ (V ) ⌘ E⌧ (V )

D(V )

bijection! CH(M) \ C�(M) \ C⌧ (M)

D(M), [g

V] ! [(g⌧ , ⇡⌧ )]

that maps orbits to orbits and which provides a natural parameterization forGrav⌧ (V ).

We give a simple generic topological condition on M , deg M = 0, wheredeg M = max{dim Ig(M) | g 2 Riem(M)} is the maximum dimension of allisometry groups Ig(M) of all Riemannian metrics g on M . This conditionguarantees that the constraint space CMC(⌧) ⌘ CH(M) \ C�(M) \ C⌧ (M) isa smooth global infinite dimensional manifold of Wheeler dimension 713 =(12�1�3�1)13. The orbit space of isometry classes of CMC(⌧) Cauchy data

1

43


(CH(M) \ C�(M) \ C⌧ (M))/D(M) is then an infinite dimensional manifold ofWheeler dimension 413 = (7�3)13 away from the orbifold type singularitieswhich occur on a nowhere dense set.

We discuss potential applications of our work to 3-manifold geometriza-tion and cosmology, which if successful, would give a dynamical reason, pro-vided by Einstein’s equations, to explain the observed fact that the universeis spatially locally homogeneous and isotropic and in such a state so as tocontinue expanding forever. In such a case, these physical aspects of our uni-verse would be a temporal asymptotic consequence of Einstein’s evolutionequations, rather than having to be imposed externally as part of a cosmo-logical principle, and thus would be a spectacular and dramatic cosmologicalconfirmation of Einstein’s equations.

2

44


Kerr–Newman Black Hole in the Formalism of IsolatedHorizons

Ales Flandera and Martin Scholtz

Institute of Theoretical Physics, Faculty of Mathematics and Physics, CharlesUniversity, Czech Republic

[email protected]

ABSTRACT

We study the Kerr-Newman black hole in the formalism of weakly isolated

horizons using a near horizon solution of Einstein’s equations. General form of

such solution has been found by Krishnan in 2012 [1]. His solution establishes

the existence of a null tetrad which is tangent to the horizon and parallelly prop-

agated off the horizon along a non-twisting null geodesic congruence. However,

the explicit construction of such tetrad for the Kerr-Newman metric is not given

in [1]. We formulate apropriate initial data and firstly construct the tetrad in

a perturbative way in the neighborhood of the horizon. Finally, we find also its

exact form everywhere in the Kerr-Newman spacetime.

References

[1] B. Krishnan, Class. Quantum Grav. 29, 205006 (2012).

1

45


The Einstein-Maxwell equations with thin layers ofpolarized or magnetized matter

Guillermo A. Gonzalez

Grupo de Investigacion en Relatividad y Gravitacion, Escuela de Fısica,Universidad Industrial de Santander, A. A. 678, Bucaramanga 680002, Colombia

[email protected]

ABSTRACT

The Einstein-Maxwell equations for material media when there is a thin layer

of polarized or magnetized matter are presented. By taking for the energy-

momentum tensor of polarized or magnetized matter the expression presented

in [1–3], and using the formalism of tensorial distributions [4–6], discontinuity

conditions through the thin layer of matter are obtained. These conditions are

expressed as relations between the jumps of the electromagnetic potential and

field with the surface polarization-magnetization tensor. By requiring also that

the electromagnetic energy-momentum tensor will be free of quadratic singular

distributions, additional compatibility conditions electromagnetic potential and

the surface polarization-magnetization tensor. Finally, the physical implications

of the obtained conditions are analyzed.

References

[1] R. A. Grot and A. C. Eringen, Int. J. Engng. Sci. 4, 639 (1966).

[2] G. A. Maugin, Ann. Inst. Henri Poincare 15, 275 (1971).

[3] G. A. Maugin, J. Math. Phys. 19, 1198 (1978).

[4] A. Papapetrou and A. Hamouni, Ann. Inst. Henri Poincare 9, 179 (1968).

[5] A. Lichnerowicz, C.R. Acad. Sci. 273, 528 (1971).

[6] A. H. Taub, J. Math. Phys. 21, 1423 (1980).

1

46


The causal boundary under the action of isometric groupactions

Jonatan Herrera Fernandez

Departamento de Matematicas, Universidad de Cordoba, [email protected]

ABSTRACT

We discuss how an isometry group G acting freely and properly discontinu-

ously on a spacetime V affects its causal completion. Concretely, we study the

principal covering projection π : V → M , where M = V/G is again a Lorentz

manifold with the induced metric. We show, by means of an example, that such

a map cannot be extended in general to the corresponding causal completions.

However, under certain mild hypotheses we can ensure both the existence of

such an extension and its continuity. Moreover, the extended map allows us to

define a homeomorphism which is also a chronological isomorphism between the

causal completion of M and a suitable quotient of the causal completion of V .

Finally, we present some applications of this result by considering certain iso-

metric group actions over Robertson-Walker spacetimes, including the Anti-de

Sitter model.

This presentation is based on joint work with L. Ake (U. Malaga) [1].

References

[1] L. Ake, J. Herrera, Spacetime coverings and the causal boundary. Journalof High Energy Physics (2017) 2017:51.

1

47


Specific solutions to Quadratic Gravity

Ondrej Hruska, Michal Karamazov, Robert Svarc

Institute of Theoretical Physics, Faculty of Mathematics and Physics,Charles University

[email protected], [email protected], [email protected]

ABSTRACT

One of the extensions of Einstein’s theory is the Quadratic Gravity, where the

action contains additional terms that are quadratic combinations of Riemann

tensor and its contractions [1], [2]. A metric that admits a non-expanding,

non-twisting and shear-free null geodesic congruence is called the Kundt met-

ric [3]. Its definition is purely geometrical and it does not depend on the field

equations; inserting the Kundt metric into Quadratic Gravity field equations

then gives us restrictions on the metric [4]. We focus on the vacuum solutions

with a cosmological constant. We study specific subcases of the Kundt metric

in Quadratic Gravity, such as the pp-waves and VSI spacetimes, and look for

their geometrical and physical interpretation.

References

[1] Deser, S. and B. Tekin, Energy in Generic Higher Curvature Gravity Theories,Phys. Rev. D 67, 084009 (2003).

[2] Malek, T. and V. Pravda, Types III and N solutions to quadratic gravity,Phys. Rev. D 84, 024047 (2011).

[3] Podolsky, J. and R. Svarc, Algebraic structure of Robinson–Trautman andKundt geometries in arbitrary dimension, Class. Quant. Grav. 32, 015001(2015).

[4] Podolsky, J. and R. Svarc, Kundt and Robinson–Trautman spacetimes inquadratic gravity, Preprint (2016).

1

48


Perception tensor and Hawking versus Unruh effect near ablack hole

Gil Jannes

Departamento de Ciencias y Tecnologıa, Universidad Europea de Madrid

ABSTRACT

We show that it is possible to define an objective, tensorial quantity cor-

responding to a seemingly subjective quantity, namely the particle perception

by different observers in a black-hole spacetime [1]. The definition of such a

PeRSET (Perception Renormalized Stress-Energy Tensor) allows for a clean

separation between the Hawking and Unruh effects near a black hole. As a re-

sult, a detector with a generic horizon-crossing trajectory will suffer a buoyancy

force. Surprisingly, when the horizon crossing is attempted at sufficiently low

velocity, this buoyant effect could even be strong enough to prevent the horizon

crossing altogether. [2].

References

[1] L. C. Barbado, C. Barcelo, L. J. Garay and G. Jannes, “A tensorial descrip-tion of particle perception in black-hole physics,” Phys. Rev. D 94, 064004(2016)

[2] L. C. Barbado, C. Barcelo, L. J. Garay and G. Jannes, “Hawking versusUnruh effects, or the difficulty of slowly crossing a black hole horizon,” JHEP1610, 161 (2016)

1

49


An Ocean Drum: energetics and dynamics in aPhysical Oceanography-Gravitation dialogue

Jose Luis Jaramillo

Institut de Mathematiques de Bourgogne (IMB)[email protected]

ABSTRACT

The main goal of this talk is to discuss a physical setting where mutual

transfer of concepts and tools between Physical Oceanography and Gravita-

tional Physics seems appropriate. Specifically, we revisit the description of the

(mesoscale) slow motions in the ocean, in the setting of the so-called quasi-

geostrophic equations, by adopting a geometric perspective akin to the relativistic

treatments of Gravity [1]. In a first stage, we introduce an effective Rieman-

nian metric in the ocean basin allowing for a rewriting of quasi-geostrophic

energetics in terms of the spectral problem of the associated Laplace-Beltrami

operator. This leads to a toy model naturally admitting an equilibrium statistical

mechanics treatment, aiming at a thermodynamical approach for the study of

stratification and topographic features in the deep ocean. In a second stage, we

briefly discuss the possible insights that this problem might offer into two dis-

tinct gravitational settings: i) stability of apparent black hole horizons, and ii)

propagation of fields on a slowly evolving spacetime background in “wave-mean

flow” theory approach.

References

[1] J.L. Jaramillo, An Ocean Drum: quasi-geostrophic energetics from a geomet-ric perspective, J. Phys. A: Math. Theor. 49, 194005 (2016).doi: 10.1088/1751-8113/49/19/194005

1

50


Definitions and examples of Finsler spacetimes

Miguel Angel Javaloyes Victoria

Department of Mathematics, University of [email protected]

ABSTRACT

We will analyze the different definitions of Finsler spacetimes provided by

Beem [3], Asanov [2], Pfeifer-Wohlfarth [7], Kostelecky [6], Javaloyes-Sanchez

[4], Amir-Aazami [1], describing their advantages and disadvantages in every

case, and what type of results can be obtained. Finally we will describe how to

generate a big quantity of examples in order to test the theory [5].

References

[1] A. B. Aazami and M. A. Javaloyes, Penrose’s singularity theorem in aFinsler spacetime, Classical Quantum Gravity, 33 (2016), pp. 025003, 22.

[2] G. S. Asanov, Finsler geometry, relativity and gauge theories, FundamentalTheories of Physics, D. Reidel Publishing Co., Dordrecht, 1985.

[3] J. K. Beem, Indefinite Finsler spaces and timelike spaces, Canad. J. Math.,22 (1970), pp. 1035–1039.

[4] M. A. Javaloyes and M. Sanchez, Finsler metrics and relativistic space-times, Int. J. Geom. Methods Mod. Phys., 11 (2014), p. 1460032 (15 pages).

[5] M. A. Javaloyes and M. Sanchez, Definition and examples of Finslerspacetimes. Preprint, 2017.

[6] V. A. Kostelecky, Riemann-Finsler geometry and Lorentz-violating kine-matics, Phys. Lett. B, 701 (2011), pp. 137–143.

[7] C. Pfeifer and M. Wohlfarth, Causal structure and electrodynamics onfinsler spacetimes, Phys. Rev. D, 84 (2011).

1

51


Higher-dimensional NUT-like and near-horizon geometriesfrom the Kerr–NUT–(A)dS metrics

Ivan Kolar

Institute of Theoretical Physics, Faculty of Mathematics and Physics, CharlesUniversity, V Holesovickach 2, 180 00 Prague, Czech Republic

[email protected]

ABSTRACT

The Kerr–NUT–(A)dS metrics describe the gravitational fields of higher-

dimensional black holes rotating in several independent planes of rotation in the

presence of a cosmological constant and NUT parameters. In this talk, I would

like to present several limits of these metrics which we have studied recently [1].

In particular, I will focus on a class of geometries, where some roots of the met-

ric functions degenerate. I will describe our limiting procedure that leads, for

example, to the Taub–NUT–(A)dS spacetime and extreme near-horizon geome-

tries. Also, I will discuss the enhanced symmetries of the resulting spacetimes

which are manifested by the presence of supplementary Killing vectors and the

decomposition of Killing tensors into Killing vectors.

References

[1] I. Kolar and P. Krtous, NUT-like and near-horizon limits of Kerr–NUT–(A)dS, 2017, arXiv:1701.03950 [gr-qc]

1

52


Gravitational waves in cosmological spacetimes andmemory effect

Wojciech Kulczycki and Edward Malec

Instytut Fizyki Mariana Smoluchowskiego, Uniwersytet Jagiellonski, Lojasiewicza 11, 30-348 Krakow, Poland

[email protected]

ABSTRACT

We show initial data for gravitational axial waves, that are twice differentiable

but which are not C2. They generate wave pulses that interact with matter in

the radiation cosmological era. This forces the radiation matter to rotate. This

rotation is permanent — it persists after the passage of the gravitational pulse.

The observed inhomogeneities of the cosmic microwave background radiation

put a bound onto discontinuities of superhorizon metric perturbations. Smooth

initial perturbations that are at least C2 give rise to gravitational wave pulses

that do not interact with the background during the radiation epoch. [1].

References

[1] Wojciech Kulczycki and Edward Malec, Axial gravitational waves in FLRWcosmology and memory effect, arXiv:1706.09620

1

53


EFT of PNG with a spin&

From YM theory to GR: The classical double copy

Michele Levi

Institut de Physique Theorique, CEA Saclay, Universite Paris-Saclay,91191 Gif-sur-Yvette, France

[email protected]

ABSTRACT

1. EFT of PNG with a spin The recent observations of GW signals

emitted by coalescing black hole binaries reinforced the need to get hold of

the analytical description of binary systems made of spinning objects at the

inspiral phase by the post-Newtonian (PN) approximation of Gravity (PNG).

We have entered a new era of high precision GW observations, for which PN

corrections and their related gauge invariant observables are required to high

orders. To this end, we present the main ideas of the Effective Field Theory

(EFT) approach to the PN formalism of the binary inspiral problem, where we

formulated an EFT for gravitating spinning objects. In particular, we present

the complete framework, which we dub “EFT of PNG”, also in terms of its

useful automatization from the fundamental theory stages to the extraction

of Hamiltonians, EOMs, and other gauge invariant observables, such as the

binding energy, and the conserved integrals of motion.

2. From Yang-Mills theory to GR: The classical double copy In

recent years powerful and intriguing duality and correspondence relations have

been discovered in the context of scattering amplitudes in supergravity theories.

The so called color-kinematics duality, and the related double copy correspon-

dence, state that once written in a specific dual form, Yang-Mills amplitudes

can be mapped onto their gravity theory counterparts by applying a prescribed

set of color to kinematics replacement rules. Beyond the opportunity to reveal

more on the underlying origin of these relations at the fundamental level of

the theories, and thus improve our current understanding of gravity, this corre-

spondence offers a compelling novel approach to handle perturbative (and exact)

computations in classical gravity, and in particular also for BHs and GWs. We

will present our first implementations of the classical double copy in gravity.

1

54


Chaos of the bound-states in anti-de Sitter spacetime

Jorge Lopes

CENTRA, Instituto Superior [email protected]

ABSTRACT

Chaos is an emergent phenomenon in a wide variety of nonlinear scenarios,

and we will demonstrate that the scalar field in AdS is no exception. We will

give numerical evidences for the presence and properties of chaos in AdS. The

presence of chaos in AdS is critical to understand the thermalization process

because the chaotic behaviour may prevent the field to collapse to a black hole.

1

55


Throat quantization of theSchwarzschild-Tangherlini(-AdS) black hole

Hideki Maeda

Department of Electronics and Information Engineering, Hokkai-GakuenUniversity, Sapporo 062-8605, Japan

[email protected]

ABSTRACT

Adopting the throat quantization pioneered by Louko and Makela [1], we de-

rive the mass and area spectra for the arbitrary-dimensional Schwarzschild-

Tangherlini black hole and its AdS and topological generalizations in the sta-

tionary state [2]. While area/entropy is equally spaced for asymptotically flat

black holes, mass is equally spaced in the asymptotically AdS case. We also in-

vestigate physical properties of the toroidal AdS black hole in the non-stationary

state described by exact wave functions [3].

References

[1] J. Louko and J. Makela, Phys. Rev. D 54, 4982 (1996).

[2] G. Kunstatter and H. Maeda, Class. Quant. Grav. 31, 115009 (2014).

[3] H. Maeda and G. Kunstatter, in preparation.

1

56


A holographic stress-energy tensor near the Cauchyhorizon inside a rotating black hole

Kengo Maeda

Faculty of Engineering, Shibaura Institute of Technology, Saitama, 330-8570,[email protected]

ABSTRACT

We investigate a stress-energy tensor for a CFT at strong coupling inside

a small five-dimensional rotating Myers-Perry black hole with equal angular

momenta by using the holographic method. As a gravitational dual, we per-

turbatively construct a black droplet solution by applying the “derivative expan-

sion” method, generalizing the work of Haddad [4], and analytically compute the

holographic stress-energy tensor for our solution. We find that the stress-energy

tensor is finite at both the future and past outer (event) horizons, and that the

energy density is negative just outside the event horizons due to the Hawking

effect. Furthermore, we apply the holographic method to the question of quan-

tum instability of the Cauchy horizon since, by construction, our black droplet

solution also admits a Cauchy horizon inside. We analytically show that the

null-null component of the holographic stress energy tensor negatively diverges

at the Cauchy horizon, suggesting that a singularity appears there, in favor of

strong cosmic censorship.

References

[1] N. Haddad, “Black Strings Ending on Horizons,” Class. Quantum Grav. 29(2012) 245001.

[2] W. A. Hiscock, “Stress-energy tensor near a charged, rotating, evaporatingblack hole,” Phys. Rev. D 15 (1977) 3054.

[3] J. Maldacena, “The Large N limit of superconformal field theories and super-gravity” Adv. Theor. Math. Phys. 2 (1998) 231, O. Aharony, S. Gubser, J.Maldacena, H. Ooguri, and Y. Oz, “Large N field theories, string theory andgravity” Phys. Rep. 323 (2000) 183.

[4] N. Haddad, “Hawking Radiation from Small Black Holes at Strong Couplingand Large N,” Class. Quantum Grav. 30 (2013) 195002.

1

57


Energy problem in the regular black hole spacetimes

V.S. Manko

Departamento de Fısica, Centro de Investigacion y de Estudios Avanzados delIPN, A.P. 14-740, 07000 Ciudad de Mexico, Mexico

[email protected]

E. Ruiz

Instituto Universitario de Fısica Fundamental y Matematicas, Universidad deSalamanca, 37008 Salamanca, Spain

[email protected]

ABSTRACT

We discuss an important property of various known singularity-free models of

black holes obtained in the framework of Einstein’s gravity coupled to nonlinear

electromagnetism — the equality of the total electromagnetic energy to the total

mass [1]. We show that this property is characteristic of a large family of

solutions of this type.

References

[1] V.S. Manko and E. Ruiz, Phys. Lett. B 760 (2016) 759.

1

58


Stirring a black hole

Julija Markeviciute†, and Jorge E. Santos

DAMTP, University of [email protected]

ABSTRACT

I will present novel asymptotically AdS4 solutions, constructed by turning on

a dipolar differential rotation at the conformal boundary. At fixed energy and

boundary profile, we find two different geometries: a horizonless AdS soliton,

and a deformed black hole with zero net angular momentum, both of which exist

up to some maximum amplitudes of the boundary profile. For sufficiently high

temperatures, the large black holes are elastic and have an extended hourglass

shape. At the maximum amplitude, these hot, large black holes develop an

ergoregion attached to the boundary, which signals a superradiant instability.

I will discuss the full phase diagram, including the possibility of phases with

disconnected horizons, by considering the Mathisson-Papapetrou equations for

a spinning test particle. Finally, I will comment on the possible implications of

this work for weak cosmic censorship.

1

59


Black hole formation with a conformally coupled scalarfield in three spacetime dimensions

Cristian Martınez

Centro de Estudios Cientıficos (CECs), Av. Arturo Prat 514, Valdivia, [email protected]

ABSTRACT

We study the black hole formation in three spacetime dimensions by consid-

ering a self-interacting scalar field conformally coupled to gravity in presence

of a negative cosmological constant. We find two classes of time-dependent

exact solutions. The first class contains configurations that evolve to a known

static hairy black hole [1, 2], and also includes the particular solution recently

obtained in [3]. The second type is characterized by solutions with a vanish-

ing energy-momentum tensor, which represent a stealth scalar field overflying

a BTZ black hole [4].

References

[1] C. Martınez and J. Zanelli, “Conformally dressed black hole in (2+1)-dimensions,” Phys. Rev. D 54, 3830 (1996).

[2] M. Henneaux, C. Martınez, R. Troncoso and J. Zanelli, “Black holes andasymptotics of 2+1 gravity coupled to a scalar field,” Phys. Rev. D 65, 104007(2002).

[3] W. Xu, “Exact black hole formation in three dimensions,” Phys. Lett. B 738,472 (2014).

[4] E. Ayon-Beato, C. Martınez and J. Zanelli, “Stealth scalar field overflying a(2+1) black hole,” Gen. Rel. Grav. 38, 145 (2006).

1

60


Black Holes in the Generalized Proca Theory

Masato Minamitsuji

Centro Multidisciplinar de Astrofisica - CENTRA, Instituto Superior Tecnico -IST, Universidade de Lisboa - UL, Avenida Rovisco Pais 1, 1049-001, Portugal

[email protected]

ABSTRACT

We investigate static and spherically symmetric black hole solutions in the

generalized Proca theory which corresponds to the generalization of the shift-

symmetric scalar-tensor Horndeski theory to the vector-tensor theory [1]. Any

solution obtained in this paper possesses a constant spacetime norm of the vec-

tor field, X := −12gµνAµAν = X0 = constant. The solutions in the theory

with generalized quartic coupling G4(X) generalize the stealth Schwarzschild

[2] and the Schwarzschild- (anti-) de Sitter [3] solutions obtained in the the-

ory with the nonminimal coupling to the Einstein tensor GµνAµAν . While in

the vector-tensor theory with the coupling GµνAµAν the electric charge does

not explicitly affect the spacetime geometry, in more general cases with nonzero

G4XX(X0) 6= 0 this property does not hold in general. The solutions in the

theory with generalized cubic coupling G3(X) are given by the Schwarzschild-

(anti-) de Sitter spacetime, where the dependence on G3(X) does not appear in

the metric function.

References

[1] L. Heisenberg, JCAP 1405, 015 (2014) doi:10.1088/1475-7516/2014/05/015[arXiv:1402.7026 [hep-th]].

[2] J. Chagoya, G. Niz and G. Tasinato, Class. Quant. Grav. 33, no. 17, 175007(2016) doi:10.1088/0264-9381/33/17/175007 [arXiv:1602.08697 [hep-th]].

[3] M. Minamitsuji, Phys. Rev. D 94, no. 8, 084039 (2016)doi:10.1103/PhysRevD.94.084039 [arXiv:1607.06278 [gr-qc]].

1

61


Innermost stable circular orbits in dilatonicEinstein-Gauss-Bonnet theory

Sindy Mojica1

in collaboration with Burkhard Kleihaus2, Jutta Kunz2 andGuillermo A. Gonzalez1

1Grupo de Investigacion en Relatividad y Gravitacion, Escuela de Fısica,Universidad Industrial de Santander, A.A. 678, Bucaramanga 680002, Colombia.

2Institut fur Physik, Universitat Oldenburg, D-26111 Oldenburg, [email protected]

ABSTRACT

Rapidly rotating compact objects are considered laboratories to test General

Relativity and theories beyond. Motivated by string theory astrophysical com-

pact objects in dilatonic Einstein-Gauss-Bonnet theory (dEGB) were studied in

[1],[2],[3],[4] showing the effects of the dilaton on the astrophysical signatures

of black holes and neutron stars. Solutions in General Relativity are compared

with the results obtained in dEGB, especially the innermost stable circular orbit

(ISCO) which is affected by the presence of the scalar field. It is expected that

such effects might be observable in astrophysical systems.

References

[1] Kleihaus, Burkhard and Kunz, Jutta and Mojica, Sindy, Quadrupole mo-ments of rapidly rotating compact objects in dilatonic Einstein-Gauss-Bonnettheory, PhysRevD.90.061501, 2014.

[2] Kleihaus, B. and Kunz, J. and Mojica, S. and Zagermann, M., Rapidly Ro-tating Neutron Stars in Dilatonic Einstein-Gauss-Bonnet Theory, Phys. Rev.D 93, 064077, 2016.

[3] Kleihaus, Burkhard and Kunz, Jutta and Radu, Eugen, Rotating Black Holesin Dilatonic Einstein-Gauss-Bonnet Theory, PhysRevLett.106.151104, 2011.

[4] Kleihaus, Burkhard and Kunz, Jutta and Moica, Sindy and Radu, Eu-gen, Spinning black holes in Einstein-Gauss-Bonnet-dilaton theory: non-perturbative solutions, Phys. Rev. D 93, 044047, 2016.

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62


Absorption of scalars by black holes in string theory

Filipe Moura

Centro de Matematica da Universidade do Minho,Escola de Ciencias, Campus de Gualtar,

4710-057 Braga, [email protected]

ABSTRACT

We show that the low frequency absorption cross section of minimally coupled

test massless scalar fields by extremal spherically symmetric black holes in d di-

mensions is equal to the horizon area, even in the presence of string–theoretical

α′ corrections. Classically one has the relation σ = 4GS between that absorp-

tion cross section and the black hole entropy. By comparing in each case the

values of the horizon area and Wald’s entropy, we discuss the validity of such

relation in the presence of higher derivative corrections for extremal black holes

in many different contexts: in the presence of electric and magnetic charges;

for nonsupersymmetric and supersymmetric black holes; in d = 4 and d = 5

dimensions. The examples we consider seem to indicate that this relation is

not verified in the presence of α′ corrections in general, although being valid in

some specific cases (electrically charged maximally supersymmetric black holes

in d = 5). We argue that the relation should be valid for the absorption cross

section of scalar fields which are part of the model (and not “test”), at least in

string theory.

References

[1] F. Moura, Absorption of scalars by extremal black holes in string theory,submitted to Gen. Rel. Grav. [arXiv:1406.3555 [hep-th]].

[2] F. Moura, Absorption of scalars by nonextremal charged black holes in stringtheory, Gen. Rel. Grav. 47 (2015) 12, 148 [arXiv:1406.2012 [hep-th]].

[3] F. Moura, Scattering of spherically symmetric d-dimensional α′−correctedblack holes in string theory, JHEP 1309 (2013) 038 [arXiv:1105.5074

[hep-th]].

1

63


Initializing gravitational evolutions withinthe parabolic-hyperbolic formulation – black holes binary

Anna Nakonieczna

Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, [email protected]

ABSTRACT

The parabolic-hyperbolic formulation of the initial data of the Einstein equa-

tions for multiple black holes systems has been proposed recently [1–3]. It pro-

vides an alternative to the traditional conformal method [4]. During the talk,

a numerical implementation of the above-mentioned evolutionary approach to

the initial data problem of general relativity will be presented. It will involve

a binary system composed of superposed Kerr-Schild black holes.

References

[1] I.Racz, Constraints as evolutionary systems, Class. Quant. Grav. 33, 015014(2016).

[2] I.Racz, A simple method of constructing binary black hole initial data,arXiv:1605.01669 (2017).

[3] I.Racz, On the ADM charges of multiple black holes, arXiv:1608.02283 (2017).

[4] G.B.Cook, Initial data for numerical relativity, Living Rev. Rel. 3, 5 (2000).

1

64


Advanced wave extraction algorithmsin numerical relativity

Andrea Nerozzi

Centro Multidisciplinar de Astrofısica - CENTRA, Departamento de Fısica,Instituto Superior Tecnico - IST, Universidade de Lisboa - UL, Avenida Rovisco

Pais 1, 1049-001 Lisboa, [email protected]

ABSTRACT

With the recent detection of gravitational waves and the expected improve-

ments in accuracy of current and future experiments, it is of primary impor-

tance that numerical simulations achieve higher degrees of accuracy as well.

In particular, the process of extracting gravitational waveforms from numeri-

cal simulations can be still subject by possible systematic errors, mostly because

of the gauge freedom that is encountered along the way. I will present recent

results in the field of wave extraction using the Newman-Penrose (NP) formal-

ism, specifically aiming to remove all gauge ambiguities in the calculation of

the NP quantities at finite radius. I will also discuss possible extensions of this

methodology to obtain a gauge fixed signal at null infinity.

1

65


Particle collision with an arbitrarily high center-of-massenergy near a Banados-Teitelboim-Zanelli black hole

Kota Ogasawara

Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, [email protected]

ABSTRACT

We consider a particle collision with a high center-of-mass energy near a

Banados-Teitelboim-Zanelli (BTZ) black hole. We obtain the center-of-mass

energy of two general colliding geodesic particles in the BTZ black hole space-

time. We show that the center-of-mass energy of two ingoing particles can be

arbitrarily large on an event horizon if either of the two particles has a critical

angular momentum and the other has a noncritical angular momentum. We

also show that the motion of a particle with a subcritical angular momentum

is allowed near an extremal rotating BTZ black hole and that a center-of-mass

energy for a tail-on collision at a point can be arbitrarily large in a critical

angular momentum limit. [1].

References

[1] N. Tsukamoto, K. Ogasawara, and Y. Gong, Phys. Rev. D 96, 024042 (2017).

1

66


Universal electromagnetic fields

Marcello Ortaggio

Institute of Mathematics of the Czech Academy of Sciences,Zitna 25, 115 67 Prague 1, Czech Republic

ortaggio(at)math(dot)cas(dot)cz

ABSTRACT

Already in the 30s, Schroedinger observed that all null Maxwell fields solve

the equations for the electromagnetic field in any non-linear electrodynamics.

More generally, we study properties of “universal” p-forms, i.e., electromagnetic

fields that solve simultaneously any generalized electrodynamics (for which the

field equations contain arbitrary powers and derivatives of the field strenght).

Some results including the coupling to Einstein’s gravity are also discussed, and

analogies with “universal spacetimes” (which solve simultaneously virtually any

theory of gravity) mentioned.

1

67


Self-consistency of higher-order gravities

Tomas Ortın

Instituto de Fısica Teorica UAM/CSICC/ Nicolas Cabrera, 13–15, C.U. Cantoblanco, E-28049 Madrid, Spain

[email protected]

ABSTRACT

We show that, in all metric theories of gravity with a general covariant action,

gravity couples to the gravitational energy-momentum tensor in the same way it

couples to the matter energy-momentum tensor order by order in the weak field

approximation around flat spacetime. We discuss the relation of this property

to the Strong Equivalence Principle, the self-consistency problem and bootstrap.

This talk is based on ref. [1]

References

[1] T. Ortın, “Higher order gravities and the Strong Equivalence Principle,”arXiv:1705.03495 [gr-qc].

1

68


Relativistic low angular momentum accretion.

Michal Pirog

Jagiellonian [email protected]

ABSTRACT

I will report on the results of the joint numerical project with J.A. Font and

P. Mach. We investigated low angular momentum accretion of inviscid fluids

on black holes. The Newtonian calculation in this topic have been already done

by D. Proga and M. Begelman [1]. Our work promotes their models to fully

relativistic setting. The staring point of those simulations is the Bondi-type

accretion solution, perturbed by adding a small amount of angular momentum.

The results of simulations will be discussed, emphasizing the similarities and

differences with Newtonian models.

References

[1] D. Proga, M. Begelman, Accretion of Low Angular Momentum Material ontoBlack Holes: Two-dimensional Hydrodynamical Inviscid Case, Astrophys. J.582, 69 (2003).

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69


On exact solutions to quadratic gravity

Alena Pravdova


[email protected]

ABSTRACT

Quadratic gravity arises by adding corrections quadratic in the curvature

to the Einstein-Hilbert action. Corresponding field equations are considerably

more involved than the Einstein equations and as a result very few exact solu-

tions are known, mostly various generalizations of pp-waves with traceless Ricci

tensor of type N. We prove that in quadratic gravity under quite general as-

sumptions, the traceless Ricci tensor of type N or III implies that the spacetime

is Kundt, explaining thus in retrospect why virtually all known exact solutions

in quadratic gravity are Kundt. We also present examples of new Kundt and

non-Kundt vacuum solutions. We also show that static spherically symmetric

non-Schwarzschild vacuum black hole in quadratic gravity, recently discovered

by Lu, Perkins, Pope, and Stelle using numerical methods, is conformal to

Kundt and show how this simplifies mathematical description of the problem.

This talk is based on joint works with J. Podolsky, V. Pravda and R. Svarc

[1, 2].

References

[1] V. Pravda, A. Pravdova, J. Podolsky, and R. Svarc, Exact solutions toquadratic gravity, Phys. Rev. D95 (2017) 084025.

[2] J. Podolsky, V. Pravda, A. Pravdova, and R. Svarc, in preparation (2017)

1

70


Four of a kind: I-Love-Q-δM

Borja Reina

Dublin City University, Universidad del Paıs [email protected]

ABSTRACT

In a recent work [1] we applied a rigorous perturbed matching framework [2]

to show the amendment of the mass of rotating stars in Hartle’s model [3].

Here, we apply this framework to the tidal problem in binary systems [4]. Our

approach fully accounts for the correction to the Love numbers needed to obtain

the universal I-Love-Q relations [5]. This correction arises from the jump in

the first derivative of one of the functions in the perturbations at the surface of

the star, proportional to the energy density there. Hence it is relevant for linear

equations of state, used to model quark stars. The combination of this correction

for tidal numbers and the correction for the mass of rotating stars allows us to

find a universal relation involving the second-order contribution to the mass

δM . We thus complete the set of universal relations for the tidal problem in

binary systems, involving four perturbation parameters, namely I, Love, Q, and

δM . These relations can be used to obtain the perturbation parameters directly

from observational data.

References

[1] B. Reina and R. Vera (2015) Revisiting Hartle’s model using perturbedmatching theory to second order: amending the change in mass. Class. Quan-tum Grav. 32 155008.

[2] M. Mars (2005) First and second order perturbations of hypersurfaces. Class.Quantum Grav. 22 3325–3348.

[3] J. B. Hartle (1967) Slowly Rotating Relativistic Stars. I. Equations of Struc-ture. Astrophys. J. 150 1005–1029.

[4] B. Reina, N. Sanchis-Gual, R. Vera and J. A. Font (2017) Completionof the universal I-Love-Q relations in compact stars including the mass.arXiv :1702.04568

[5] K. Yagi and N. Yunes (2013) I-Love-Q: Unexpected Universal Relations forNeutron Stars and Quark Stars. Science 341 365-368

K. Yagi and N. Yunes (2014) Erratum for the Report: ”I-Love-Q: UnexpectedUniversal Relations for Neutron Stars and Quark Stars” by K. Yagi and N.Yunes Science 344 1250349

1

71


Rotating BTZ black hole assuming running couplings

Angel Rincon

Instituto de Fısica, Pontifıcia Universidad Catolica de Chile,Av. Vicuna Mackenna 4860, Santiago, Chile

[email protected]

ABSTRACT

In the present work a generalization of the rotating BTZ black hole for the case

of scale dependent couplings is studied. One starts by using the effective action

for scale dependence couplings to derive a generalization of the corresponding

Einstein field equations. Moreover, one obtains new solutions for lapse func-

tion, cosmological coupling and Newtons coupling. In addition, we show the

effect of scale dependent couplings on the classical solution. Besides, asymp-

totic behaviour as well as thermodynamic properties were computed in detail.

References

[1] B. Koch, I. A. Reyes and A. Rincon, Class. Quant. Grav. 33, no. 22, 225010(2016) doi:10.1088/0264-9381/33/22/225010 [arXiv:1606.04123 [hep-th]].

[2] A. Rincon, B. Koch and I. Reyes, J. Phys. Conf. Ser. 831, no. 1, 012007(2017) doi:10.1088/1742-6596/831/1/012007 [arXiv:1701.04531 [hep-th]].

[3] A. Rincon, E. Contreras, P. Bargueno, B. Koch, G. Panotopoulos andA. Hernandez-Arboleda, arXiv:1704.04845 [hep-th].

1

72


Dynamical spacetimes in low-energy string theory andcosmic censorship

Jorge Rocha

Departament de Fısica Quantica i Astrofısica, Institut de Ciencies del Cosmos,Universitat de Barcelona, Martı i Franques 1, E-08028 Barcelona, Spain

[email protected]

ABSTRACT

Stationary black holes in low-energy string theory have been investigated for

decades but little is known about their non-stationary counterparts. I will dis-

cuss spherically symmetric — but time-dependent — solutions of the Einstein-

Maxwell-axion-dilaton system, which arises as its low-energy effective descrip-

tion. Two new classes of exact radiating spacetimes with constant electric and

magnetic charges will be presented, and their intricate causal structure is clari-

fied. An even larger class of dynamical spacetimes describing the accretion (or

radiation) of null dust is also obtained. It is shown that, within this family

of solutions, a black hole cannot turn into a naked singularity if the null dust

satisfies standard energy conditions. This result supports the cosmic censorship

conjecture in the context of effective string theory.

1

73


A hyperbolic theory of relativistic conformal dissipativefluids

Marcelo E. Rubio∗

FaMAF – UNC, IFEG – CONICET, (5000) Cordoba, [email protected]

ABSTRACT

We develop a complete description of the class of conformal relativistic dissi-

pative fluids of divergence form, following the formalism carried out by Geroch

and Lindblom in the early 90’s. These theories are described in terms of evolu-

tion variables whose dynamics is governed by total divergence-type equations.

More specifically, we give a characterization of the whole family of conformal

fluids in terms of a single master scalar function up to second order in dissi-

pative variables. We identify the equilibrium states of the theory, and derive

the corresponding constitutive relations, as well as a Fourier-like law for heat

conduction. Finally, we prove that these type of theories is symmetric hyper-

bolic, implying that, under certain algebraic conditions, there exists a well posed

initial value problem for the evolution equations.

∗Work in collaboration with Luis Lehner and Oscar Reula.

1

74


Singular and nonsingular black holes in f(R) theories andbeyond

Diego Rubiera-Garcia

Institute of Astrophysics and Space Sciences, Lisbon University (Portugal)[email protected]

ABSTRACT

The search for regular black holes in the literature usually focus on obtain-

ing bounded curvature scalars, despite the fact that the singularity theorems are

based instead of the (in)completeness of geodesics. In this talk I consider a fam-

ily of quadratic f(R) extensions of General Relativity coupled to an anisotropic

fluid satisfying standard energy conditions to show that, in black hole space-

times obtained in these extensions, divergences in the curvature scalars are not

necessarily correlated to geodesic incompleteness. Further, using generalizations

under the form of Ricci-squared terms and Born-Infeld-type actions I show that

spacetimes containing curvature divergences are not unavoidably pathological.

1

75


Homogeneous Solutions of Minimal Massive 3D Gravity

Nihat Sadik Deger

Department of Mathematics, Bogazici University, [email protected]

ABSTRACT

In this talk we construct simply transitive homogeneous solutions of the three-

dimensional Minimal Massive Gravity (MMG) model [1]. In addition to those

that have analogs in Topologically Massive Gravity [2], such as warped AdS and

pp-waves, there are several solutions genuine to MMG. Among them, there is a

stationary Lifshitz metric with the dynamical exponent z=-1 and an anisotropic

Lifshitz spacetime where all coordinates scale differently. Moreover, we identify

a homogeneous Kundt solution at the chiral point of the theory. We also show

that in a particular limit of the physical parameters in which the Cotton tensor

drops out from the MMG field equation, homogeneous solutions exist only at the

merger point in the parameter space if they are not conformally flat.

References

[1] E. Bergshoeff, O. Hohm, W. Merbis, A.J. Routh and P.K. Townsend, MinimalMassive 3D Gravity, Class.Quant.Grav. 31 (2014) 145008, arXiv:1404.2867.

[2] S. Deser, R. Jackiw and S. Templeton, Topologically Massive Gauge Theories,Ann.Phys. 140 (1982) 372.

1

76


Ehlers-Kundt conjecture about Gravitational Waves

Miguel Sanchez

Departamento de Geometrıa y Topologıa, Univ. Granada.Facultad de Ciencias, Campus Fuentenueva s/n. E-18071 Granada (Spain)

[email protected]

ABSTRACT

Ehlers-Kundt conjecture asserts that all geodesically complete gravitational

pp-waves must be plane waves. Mathematically, it becomes equivalent to a prob-

lem on the Euclidean plane R2 with a very simple formulation in Classical Me-

chanics: given a non-necessarily autonomous potential V (z, u), (z, u) ∈ R2×R,

harmonic in z (i.e. source-free), the trajectories of its associated dynamical sys-

tem z(s) = −∇zV (z(s), s) are complete (living eternally) if and only if V (z, u)

is a polynomial in z of degree at most 2 (that is, V is a standard mathemat-

ical idealization of vacuum). Along the talk, the conjecture will be discussed

and solved in the significative case that V is bounded polynomially in z at any

u ∈ R. Based in joint work with J.L. Flores, [1].

References

[1] J.L. Flores, M. Sanchez, Ehlers-Kundt Conjecture about Gravitational Wavesand Dynamical Systems, arxiv: 1706.03855.

1

77


Analogue Gravity from Quantum potential inducedBose-Einstein Condensates (BEC): UV-IR Coupling in

Analogue Hawking radiation

Supratik Sarkar1, A. Bhattacharyay1

1 Indian Institute of Science Education and Research (IISER) - Pune, [email protected]

ABSTRACT

The presence of the Lorentz-breaking quantum potential term in the non-

local BEC model apparently gives rise to the massive scalar excitations for large

wavelength phonon modes (of O(1/ξ)) characterized by a ‘massive’ minimally

coupled free Klein-Gordon equation in the context of experimental observations

of analogue Hawking radiation where at least one spatial dimension is kept free

to allow for the source/sink of the background fluid flow [1]. Thus arising out

of a non-relativistic non-local BEC, an Analogue gravity model is formulated

upto O(ξ2) accuracy in the presence of the quantum potential term for a canon-

ical acoustic black hole in (3+1)-d spacetime. A UV-IR coupling between short

wavelength ‘primary’ modes (which are supposedly Hawking radiated through the

sonic event horizon) and the large wavelength ‘secondary’ modes is the strik-

ing upshot which is inevitable in the quantum gravity experiments of analogue

Hawking radiation in the laboratory. These ‘secondary’ modes would grow over

space by gaining energy from the Hawking radiated quanta (‘primary’ modes)

that are distinguished by their characteristic features of the respective growth

rates [2]. .

References

[1] Supratik Sarkar and A. Bhattacharyay, Phys. Rev. D 93, 024050 (2016).

[2] Supratik Sarkar and A. Bhattacharyay, arXiv 1703.08027 [gr-qc] (2017).

1

78


Area deficit of geodesic balls and gravitational energy

Jose M M Senovilla

Fısica teorica, Universidad de Paıs Vasco, Apartado 644, 48080 Bilbao, [email protected]

ABSTRACT

Gravity manifests itself as curvature of spacetime, and its strength can be

measured by considering the deficit of the volume of small geodesic balls with

respect to their counterparts in flat spacetime. The area deficit of the enclosing

boundaries can actually be put in relation, via the Einstein field equations, with

the energy density of matter at the ball’s centre, and this led Jacobson to pro-

pose a novel “maximal entanglement hypothesis”, establishing a thermodynamic

principle for quantum gravitational theories [1].

In this contribution we consider what happens when the matter energy density

vanishes. The area still feels the effect of pure gravity, and this change should

be related to the gravitational strength, or in simple words, to the gravitational

energy density with respect to the mentioned observer. The area deficit now

involves terms quadratic in the curvature related to classical quantities [2], but

there arise some subtleties and ambiguities to be resolved.

Work based on a collaboration with Ted Jacobson and Antony Speranza.

References

[1] T. Jacobson, Entanglement equilibrium and the Einstein equation, Phys. Rev.Lett. 116 (2016) 201101

[2] J.M.M. Senovilla, Super-energy tensors, Classical and Quantum Gravity 17(2000) 2799.

1

79


Quantum corrected Friedmann equations from loopquantum black holes entropy-area relation

C. A. S. Silva

Instituto Federal de Educacao, Ciencia e Tecnologia da Paraıba - CampusCampina Grande

[email protected]

ABSTRACT

Based upon the holographic principle, Jacobson demonstrated that the space-

time can be viewed as a gas of atoms with a related entropy given by the

Bekenstein-Hawking formula [1]. Following this argument, Friedmann equa-

tions can be derived by using Clausius relation to the apparent horizon of

Friedmann-Robertson-Walker (FRW) universe [2]. Loop Quantum Gravity is a

propose to description of the spacetime behavior in situations where its atomic

characteristic arises. Among these situations, the behavior of our universe near

the Big Bang singularity is described by Loop Quantum Cosmology (LQC). How-

ever, a derivation of the LQC equations based on the Bekenstein bound is lack-

ing. In this work, we obtain the quantum corrected Friedmann equations from

the entropy-area relation given by loop quantum black holes (LQBH), setting a

still absent connection between holographic and LQC descriptions of the cosmos.

Connections with braneworld cosmology have been also addressed.

References

[1] T. Jacobson, Phys. Rev. Lett. 75 (1995) 1260.

[2] R. G. Cai and S. P. Kim, JHEP 0502 (2005) 050.

1

80


Quantum Null Energy Conditionfrom Numerical Holography

Philipp Stanzer

Institute for Theoretical Physics, TU Wien, Vienna, [email protected]

ABSTRACT

Since all the classical energy conditions fail at some point, it is necessary to

improve them. The quantum null energy condition is a novel approach for a

local energy condition valid also in relativistic quantum field theories. In the

past two years several proofs for this conjecture were provided, with increasing

generality. In this talk I am going to present the first examples where the QNEC

is calculated explicitly and its (non-)saturation is studied.

In addition to the analytic result for vacuum, we were able to calculate the

entanglement entropy of a thermal state using numerical holography. Further

we investigate a system of colliding lumps of energy in which the classical null

energy condition is violated.

References

[1] “Exploring nonlocal observables in shock wave collisions,”C. Ecker, D. Grumiller, P. Stanzer, S. A. Stricker and W. van der Schee,J. High Energ. Phys. (2016) 2016: 054.doi:10.1007/JHEP11(2016)054

1

81


Wormhole models without symmetries

Otakar Svıtek

Institute of Theoretical Physics, Faculty of Mathematics and Physics, CharlesUniversity, V Holesovickach 2, 180 00 Prague 8, Czech Republic

[email protected]

ABSTRACT

We present two types of wormholes based on the Robinson–Trautman class of

spacetimes generally containing geometries without symmetries. The first one

is a global model sourced by a ghost scalar field where we study asymptotics, sta-

bility and other issues. The second one is a thin-shell model which approaches

a simple spherically symmetric wormhole in the distant future. The generaliza-

tion of the second model to higher dimensions provides a possibility of avoiding

the energy condition violation.

1

82


Spacetimes with Nonlinear Electrodynamics

Tayebeh Tahamtan

Institute of Theoretical Physics, Faculty of Mathematics and Physics, CharlesUniversity, V Holesovickach 2, 180 00 Prague 8, Czech Republic

[email protected]

ABSTRACT

Recently, substantial attention was devoted to study the role of different mod-

els of Nonlinear Electrodynamics in curing the spacetime singularities thus ob-

taining regular black holes. These models usually considered highly symmetric

situations. We would like to address the genericity of this and other features in

a more general setup. We will also study the interplay between the resolution

of curvature and electromagnetic field singularities.

1

83


Supersymmetric solution in dynamical M-brane background

Kunihito Uzawa

Department of Physics, School of Science and Technology, Kwansei GakuinUniversity, Sanda, Hyogo 669-1337, Japan

[email protected]

ABSTRACT

The supersymmetry arises in certain theories of fermions coupled to gauge

fields and gravity in a spacetime of eleven dimensions [1]. The dynamical brane

backgrounds have mainly been studied for the class of purely bosonic solutions

only [2, 3, 4], but developments involving time-dependent supersymmetric so-

lution have made it clear that one can get more information by asking what

happens on dynamical brane systems [5]. In this presentation, we show an

exact supersymmetric solution of dynamical M-brane background in the eleven-

dimensional supergravity and consider applications to dynamics of geodesic mo-

tion and black hole physics.

References

[1] E. Cremmer, B. Julia and J. Scherk, “Supergravity Theory in Eleven-Dimensions,” Phys. Lett. 76B (1978) 409.

[2] G. W. Gibbons, H. Lu and C. N. Pope, “Brane worlds in collision,” Phys.Rev. Lett. 94 (2005) 131602 [arXiv:hep-th/0501117].

[3] P. Binetruy, M. Sasaki and K. Uzawa, “Dynamical D4-D8 and D3-D7 branesin supergravity,” Phys. Rev. D 80 (2009) 026001 [arXiv:0712.3615 [hep-th]].

[4] K. i. Maeda, N. Ohta and K. Uzawa, “Dynamics of intersecting brane sys-tems – Classification and their applications –,” JHEP 0906 (2009) 051[arXiv:0903.5483 [hep-th]].

[5] H. Kodama and K. Uzawa, “Moduli instability in warped compactifications ofthe type IIB supergravity,” JHEP 0507 (2005) 061 [arXiv:hep-th/0504193].

1

84


Fractional wave operators and the wave equation inanti-de Sitter spaces

Bruno Vergara

ICMAT – Institute of Mathematical Sciences, Universidad Autonoma de [email protected]

ABSTRACT

In this talk I will discuss the connection between the fractional powers of the

standard wave operator with the problem of the massive wave equation on anti-

de Sitter spaces with boundary data at infinity. This relation can be seen as

the Lorentzian analog of well known results derived in the context of non-local

elliptic equations and conformal geometry for the fractional Laplacian. The talk

is based on a joint work with A. Enciso and M.d.M. Gonzalez [1] .

References

[1] A. Enciso, M.d.M. Gonzalez, B. Vergara. Fractional powers of the waveoperator via Dirichlet-to-Neumann maps in anti-de Sitter spaces. PreprintarXiv:1607.04390.

1

85


Covariantly Quantum Field Theory

Vincenzo Vitagliano

CENTRA - Instituto Superior Tecnico, University of Lisbon, [email protected]

ABSTRACT

The usual calculation of effective actions relies on some assumption about

the split between background and fluctuating field variables, in principle lead-

ing to a further dependence of the results on the choice of background and

gauge. Arguing that such dependence of the effective action is a by-product

of the quantum fields’ dependence on the parametrization, Vilkovisky and De-

Witt developed a geometrical, field-space covariant procedure to modify the

usual background-field method which renders the effective action gauge- and

background-independent. In this talk, I will present some modern cosmological

applications of the Vilkovisky-DeWitt method, and further suggestions about the

role of quantum corrections in astrophysical systems.

1

86


Gravitational degrees of freedom and isometric

embedding

Steven Willison

CENTRA, IST, UTL, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

Abstract

When physical space-time is treated as a submanifold embeded in ahypothetical 14 dimensional Minkowski space-time, the Einstein Equa-tions can be reformulated as a system of nonlinear wave equations in theembedding coordinate functions. We will focus on possible applications ingravitational physics and give a discussion of the initial value/constraintsproblem .

1

87


Black holes as probes for fundamental physics

Helvi Witek

Departament de Fısica Quantica i Astrofısica & Institut de Ciencies del Cosmos(ICCUB), Universitat de Barcelona, Martı i Franques 1, E-08028 Barcelona,

[email protected]

ABSTRACT

Confronting general relativity (GR) with observations, thus supporting its

role as our standard model of gravity is almost as old as the theory itself. Al-

though GR has passed all experimental tests so far, most of which were limited

to solar system or weak gravity scales, both cosmological observations and the

quest for a unified theory of quantum gravity strongly motivate extensions to

it in the strong gravity regime.

After entering the gravitational wave era in 2016 we are now in the unique

position to test gravity in its most challenging, highly dynamical regime using

black holes. To do so, however, we need to understand the black hole binary

problem in extensions of GR. In this talk I will give an update on the latest

progress concerning this problem.

1

88


New conservation laws for matter near spinning black holes

Vojtech Witzany

ZARM, Universitat Bremen, Am Falturm 2, 28359 Bremen, [email protected]

ABSTRACT

The axisymmetric and stationary Kerr space-time, which represents the

gravitational field of a spinning black hole, possesses an additional “hidden”

symmetry expressed in the existence of a Killing-(Yano) tensor. In this talk, we

show that this symmetry is connected to non-trivial conservation laws for the

evolution of test matter in Kerr space-time and use them to test the validity of

numerical simulations of relativistic hydrodynamics on the Kerr background.

1

89


Posters

90


Initial boundary value problem for the Einstein fieldequations for a class of spherically symmetric imperfect

fluids

Irene Brito, Filipe Mena

Centro de Matematica, Universidade do Minho, 4710-057 Braga, [email protected], [email protected]

ABSTRACT

We consider the initial boundary value problem for a class of spherically

symmetric imperfect fluids and prove existence and uniqueness of solutions of

the Einstein field equations [1]. This work generalizes the results obtained in

[2] for perfect fluids.

References

[1] Brito, I., Mena, F., Initial boundary value problem for the spherically sym-metric Einstein equations with fluids with tangential pressure, submitted(2017).

[2] Kind, S., Ehlers, J., Initial boundary value problem for the spherically sym-metric Einstein equations for a perfect fluid, Class. Quantum Grav. 10, 2123(1993).

1

91


Chiral vortical effect in curved space and theChern-Simons current

Antonino Flachi

Department of Physics & Research and Education Center for Natural Sciences,Keio University, Yokohama, Japan

[email protected]

ABSTRACT

In the presence of rotation, gravity induces, even at zero temperature, a chiral

vortical current. This current is interpreted as emerging from the gravitational

Chern-Simons current. We argue that this gravitational Chern-Simons chiral

vortical current may provide a novel universal microscopic mechanism behind

the generation of collimated jets from rotating astrophysical compact sources.

References

[1] A. Flachi, K. Fukushima, Chiral vortical effect in curved space and the Chern-Simons current, arXiv:1702.04753 [hep-th]

1

92


Binary boson stars and numerical relativity

Apratim Ganguly

Department of Mathematics, Rhodes University, 6140 Grahamstown, SouthAfrica

[email protected]

ABSTRACT

Recent discoveries of gravitational waves from black hole binaries were a

strong validation of general relativity in the strong-field limit. To fully con-

strain the theory, however, it is necessary to establish whether sources other

than classical black holes might potentially generate analogous signals. For ex-

ample, boson stars are an exotic matter source that arise in certain scalar-tensor

gravity theories. The advantage of studying boson stars is that they are useful

probes of strong-field gravity without facing problems associated with regular

matter such as shocks and discontinuities in fluid variables. This talk reports

on numerical studies of binary boson stars using a computational model to un-

derstand aspects of the gravitational wave signature of boson star interactions

and discusses some results from explorations of the orbital dynamics of boson

star binaries.

1

93


Informational Theory of Relativity

Akio Hosoya

Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, [email protected]

Shunsuke Fujii

Department of General Education, National Institute of Technology, TokyoCollege, Tokyo 193-0097, Japan

[email protected]

ABSTRACT

Assuming the minimal time to send a bit of information in the Einstein

synchronization of the two clocks located at different positions, we introduce

the extended metric to the information space [1] with the coordinate σ,

ds2 = gµν(x)(dxµ − uµτdσ)(dxν − uντdσ) + (a + 1)τ2(dσ)2 .

This modification of relativity changes the red shift formula keeping the geodesic

equation intact. Extending the gauge symmetry hidden in the metric to the 5-

dimensional general invariance, we start with the Einstein-Hilbert action in the

5-dimensional space-time. After the 4+1 decomposition, we obtain the effective

action which includes the Einstein-Hilbert action for gravity, the Maxwell-like

action for the velocity field uµ and the Lagrange multiplier term which ensures

the normalization of the time-like velocity field,

S = c4

16πG

∫ √−(a − gξηuξuη) det(gαβ)d4xτdσ

[gαβRαβ − gαβgρσ

4(a+1) AαρAβσ + 16πGc4

λ(gαβuαuβ + 1)],

where gαβ = gαβ + uαuβ

a+1 , Rαβ is the Ricci tensor and the field strength of the

velocity field is Aαρ := Dαuρ − Dρuα. G and C are Newton’s constant and

the light velocity. The resultant action turns out to be a particular case of the

so-called Einstein-Aether theories [2]. As an application we found a spherically

symmetric solution of the field equation, which exhibits a Schwarzschild-like

space-time but with the minimal radius. I will discuss the informational mean-

ing of the coordinate σ going back to the Einstein synchronization.

References

[1] A. Hosoya and S. Fujii, arXiv:1703.03971

[2] C. Eling, T. Jacobson, Class.Quant.Grav. 23 (2006) 5625-5642, Erratum:Class.Quant.Grav. 27 (2010) 049801 [gr-qc/0603058]

1

94


Relativistic BHL Accretion in the Presence of Stellar Winds andDense Clumps Around a Black Hole

F. D. Lora-Clavijo and A. Cruz-Osorio

Grupo de Investigacion en Relatividad y Gravitacion, Escuela de Fısica,Universidad Industrial de Santander, A. A. 678, Bucaramanga 680002, Colombia.

[email protected]

ABSTRACT

In the astrophysical context, relativistic Bondi-Hoyle-Lyttleton (BHL) accretion has

been used to study different processes, from the vibrations in the shock cone, which may

potentially explain high energy phemomena like QPOs [1, 2, 3, 4], to ultra-relativistic

processes associated with the growth of primordial BHs during the radiation era [5,

6]. Given the importance of undertanding the accretion process, the relativistic BHL

problem has been also studied in the presence of magnetic fields [7], radiative terms [8],

and with density or velocity gradients [9, 10]. In this work, we study the relativistic

BHL accretion onto a Schwarzschild black hole, which is surrounded by rigid and small,

randomly distributed, bodies. These bodies are idealized representations of substructure

like bubbles created by stellar winds or cold clumps. We consider cases where the flow

moves supersonically towards the black hole. The interaction with these rigid obstacles

transforms ram pressure of the flow into thermal pressure through bow shocks, slowing

down the flow and making the accreting gas turbulent. As a consequence, although the

flow reaches a fairly steady state, the accretion rate presents some variability.

References

[1] Donmez O., Zanotti O., Rezzolla L., 2011 MNRAS, 412, 1659

[2] Cruz-Osorio A., Lora-Clavijo F. D., Guzman F. S., 2012, MNRAS, 426, 732

[3] Donmez O., 2012, MNRAS, 426, 1533

[4] Lora-Clavijo F. D., Guzman F. S., 2013, MNRAS, 429, 3144

[5] Penner A. J., 2013, MNRAS, 428, 2171

[6] Cruz-Osorio A., Lora-Clavijo F. D., Guzman F. S., 2013, AIP ConferenceSeries Vol. 1548, pp 323-327

[7] Penner A. J., 2011, MNRAS, 414, 1467

[8] Zanotti O., Roedig C., Rezzolla L., Del Zanna L., 2011, MNRAS, 417, 2899

[9] Lora-Clavijo F. D., Cruz-Osorio A., Moreno Mendez E., 2015, ApJS, 219, 30

[10] Cruz-Osorio A., Lora-Clavijo F. D., 2016, MNRAS, 460, 3193

1

95


Pseudospherical surfaces based on the GrapheneSuperlattice Equation

Martin-Vergara, F., Rus, F., and Villatoro, F. R.

Lenguajes y Ciencias de la Computacion. Universidad de Malaga, 29071 [email protected], [email protected], [email protected]

ABSTRACT

The sine-Gordon equation (sGeq) describe a relativistic scalar field in 1+1

dimensions. Its solutions can be interpreted as pseudospherical surfaces [1].

This geometric interpretation was introduced by Lamb [2] and it is applicable

to other evolution equations with soliton solutions [3]. Electromagnetic solitary

waves can propagate in a graphene superlattice i.e., a sheet of graphene de-

posited on a superlattice, with periodically alternating layers of SiO2 and h-BN,

under THz radiation. The nonlinear d’Alembert equation for the dimensionless

z-component of the electromagnetic vector potential is the following graphene

superlattice equation (GSLeq):

∂2α

∂t2− c2

∂2α

∂x2+

ω20 b

2 sinα√1 + b2 (1− cosα)

= 0,

as derived by Kryuchkov and Kukhar’ [4]; this equation is a generalization of the

sGeq, where ω20 is the normalized frequency, b ≤ 1 is a geometrical parameter of

the superlattice, c is the speed of light, x is position and t is time. The GSLeq has

a solitary wave solution of the form α(x, t) = α(φ), where φ = x−ct. The GSLeq

is nonintegrable but can be understood as a perturbation of the sGeq for small

b. The kinks, antikinks and breathers of the sGeq correspond to solitary wave

solutions of the GSLeq. Such solutions can be interpreted as pseudospherical

surfaces, like those of the sGeq. Here, we study such surfaces and compare

them with those of the sGeq.

References

[1] R.Sasaki, ”Soliton equations and pseudospherical surfaces” Nuclear Phys.B154: 343-357 (1979).

[2] G. L. Lamb Jr., ”Solitons on moving space curves” J. Math. Phys. 18: 1654-1661 (1977).

[3] A. Sym, J. Corones, ”Lie-Group Explanation of Geometric Interpretations ofSolitons” Phys. Rev. Lett. 42: 1099-1102 (1979).

[4] S. V. Kryuchkov and E.I. Kukhar’, ”The solitary electromagnetic waves inthe graphene superlattice”, Phys. B: Condensed Matter, 408: 188-192 (2013).

1

96


Universal spacetimes

Vojtech Pravda


[email protected]

ABSTRACT

Universal spacetimes simultaneously solve vacuum field equations of all the-

ories of gravity with the Lagrangian being a polynomial curvature invariant

constructed from the metric, the Riemann tensor and its covariant derivatives

of an arbitrary order. We present several results on universal spacetimes. While

for type N and III the results are dimension independent, for type II we con-

struct universal metrics only for composite number dimensions and prove the

non-existence for five dimensions. The existence of type II universal spacetimes

for prime number dimensions remains open.

We also discuss recent results on four-dimensional universal spacetimes. We

show that in this case, universal spacetimes are necessarily algebraically spe-

cial and Kundt. We find necessary and sufficient conditions for universality

for Petrov types III and D and discuss type II universal spacetimes. Explicit

examples of universal metrics of various algebraic types are also given.

These results were obtained in collaboration with S. Hervik, T. Malek and

A. Pravdova [1, 2, 3].

References

[1] S. Hervik, V. Pravda, and A. Pravdova, Type III and N universal spacetimes,Class. Quantum Grav. 31 (2014) 215005.

[2] S. Hervik, T. Malek, V. Pravda, and A. Pravdova, Type II universal space-times, Class. Quantum Grav. 32 (2015) 245012.

[3] S. Hervik, V. Pravda, and A. Pravdova, Universal spacetimes in four dimen-sions, arXiv: 1707.00264

1

97


Conformal scalar invariants of weight zero

Ignacio Sanchez–Rodrıguez

Department of Geometry and Topology, University of Granada, [email protected]

ABSTRACT

In a lesser known paper [1] Albert Einstein announces that it is possible to add

an equation to the field equations of General Relativity. We explore this sugges-

tion from a geometrical point of view, and then we obtain a family of conformal

scalar differential invariants of weight 0 for generic (pseudo-)Riemannian me-

trics in more than three dimensions.

References

[1] A. Einstein, Berliner Ber. 1921, pp. 261-264.

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98


Entropic corrected Newton’s law of gravitation

C.A.S.Silva

Instituto Federal de Educacao, Ciencia e Tecnologia da Paraıba (IFPB), CampusCampina Grande - Rua Tranquilino Coelho Lemos, 671, Jardim Dinamerica I.

R.G.L.Aragao

Departamento de Fısica, Universidade Federal de Campina Grande (UFCG),Caixa Postal 10071, 58109-970 Campina Grande, Paraıba, Brazil

ABSTRACT

The entropic interpretation of gravity introduced by Verlinde has provide a

way to derive the Newton’s law of gravitation from the Bekenstein-Hawking

entropy-area formula [1]. It is well known, on the other hand, that such for-

mula can be affected by quantum gravity corrections. As a consequence, one

may hope that such corrections can influence the Newton’s gravitational law. In

this sense, the entropic approach to the Newton’s law could be a fertile frame in

order to test the validity of quantum corrections to ordinary gravity in regimes

accessible to observations. In this work, by using the nonrelativistic Verlinde’s

approach, we obtain a quantum gravity corrected Newton’s law from the entropy-

area relation given by loop quantum black holes, a semiclassical black hole so-

lution that emerges from Loop Quantum Gravity [2]. Besides, in the sense of

relate our investigations with the current experimental activity, we discuss the

quantum mechanical properties of a gravitational atom formed by a light neutral

elementary particle [3] orbiting a loop quantum black hole. The results present

in this work have been published the reference [4].

References

[1] E. P. Verlinde, ”On the Origin of Gravity and the Laws of Newton,”JHEP1104 (2011) 029 [arXiv:1001.0785 [hep-th]]

[2] MODESTO, L.; PREMONT-SCHWARZ, I. Self-dual black holes in loopquantum gravity: Theory and phenomenology. Physical Review D, APS, v.80, n. 6, p. 064041, 2009.

[3] V. V. Flambaum and J. C. Berengut, ”Atom made from charged elementaryblack hole,” Phys. Rev. D63 (2001) 084010 doi:10.1103/PhysRevD.63.084010[gr-qc/0001022].

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