Numerical Relativity in Fundamental Physics

Ulrich Sperhake

DAMTP University of Cambridge

Gravity@Malta COST action University of Malta, 23 Jan 2018

1

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 690904, from H2020-ERC-2014-CoG Grant No. ”MaGRaTh"

646597, from NSF XSEDE Grant No. PHY-090003 and from STFC Consolidator Grant No. ST/L000636/1.

Overview⚫ Motivation

⚫ Particle Laboratories in Outer Space

⚫ Boson Stars

⚫ Compact Objects in Modified Gravity

⚫ High-Energy Collisions of Black Holes

⚫ Fundamental Properties of Spacetimes

⚫ Concluding Remarks

Motivation

A Tale of Two Pillars

⚫ Successful: pp Collisions, Solar System, Cosmology, GWs,…

Rotation Curves, Grav.Lensing, CMB, X-Ray Obs. of Halos

Not explained by Gravity of visible Matter

Dark Energy, Dark Matter and/or Modified Gravity

Cosm.Constant Problem: Why is so small and why

Hierarchy Problem: Why is Gravity so feeble?

!

⇤ ⇢dark ⇠ ⇢mat

SM of Particle Physics General Relativity

⚫ And yet: QM and Gravity not compatible + Problems or Gaps:

!

Particle Laboratories in Outer Space

Dark Matter Searches⚫ DM Candidates: Primordial BHs, LIGO BHs, WIMPs, WISPs,…

⚫ Many particle searches under way at LHC,…

⚫ Ultralight fields (WISPs):

Axions, Dark Photons, Q-balls, Bosonic Condensations,…

Compton Wavelength:

⚫ No-hair theorems limit BH-fund.field interaction, but:

Long-lived states of scalar/vector fields, Hairy BHs, super radiance

Okawa et al 1401.1548, Herdeiro & Radu 1403.2757, Zel’dovich 1971

Runaway instabilities: e.g. BH bomb Press & Teukolsky 1972

⚫ BH as atom

⚫ Search for DM through GW observations!

m ⌧ 1 eV

m ⇠ 10�10 . . . 10�20 eV ! � ⇠ 1 km . . . 102 AU

!

Superradiance⚫ Amplification of field if

akin to Penrose process

⚫ BH spins Constraints on photon mass

Pani & Cardoso 1209.0465

⚫ Superradiance also amplifies GWs East et al 1312.4529

⚫ Floating orbits Press & Teukolsky 1972

⚫ Nonlinear study of Proca field East & Pretorius 1704.04791

of BH mass extracted; saturation when

⚫ TODO: GW signature of fundamental fields in BH mergers?

⚫ Fund.fields can also pile up at centre of stars Brito et al 1508.04773

! < m⌦BH

!

! > 9% m⌦BH & !

Boson Stars

Basic properties⚫ EM solitons: Geons Wheeler 1955 but unstable!

⚫ Self-gravitating complex scalar field: Klein-Gordon Geons

Kaup 1968 Now called Boson Stars

⚫ Mini Boson Stars:

diagram; cf. Neutron Stars

Scaling with :

⚫ Self-interaction wider range of models

E.g. :

⚫ Rotating BSs: angular mom. per particle number = Integer

Quantum nature

⚫ Oscillatons: localized, oscillating real scal.fields

� / ei!t , V (�) = m |�|2

Eby et al 1511.04474

M �RM

max

= 0.633M2Planck

/mm

!

� |�|4/4 Mmax

⇡ (0.1GeV2)M��1/2/m2 Colpi et al 1986

!

Seidel & Suen 1991

Boson star inspirals⚫ Potential (“nontopological solitonic BSs”):

⚫ Superpose two single BS solutions; conformal

⚫ Phase shift : Stars almost completely annihilate

Otherwise: Rotating bar relaxing to a non-rotating BS

Bezares et al 1705.01071

⚫ Inspiral waveforms

⚫ TODO: systematic

waveform modeling

V (�) = m|�|2 + �|�|4

BH formation or…

Oscillating BSs

Palenzuela 1710.09432

Z4

⇡

Compact objects in modified gravity

Range of theories⚫ Classify theories through Lovelock’s theorem

⚫ Prerequisite: Well-posed initial value formulation!

Most NR work restricted to scalar-tensor theory

Berti 1501.07274

Scalar tensor theory⚫ Spontaneous scalarization:

Consider equilibrium NS models

Abrupt increase of scalar charge for some parameter range

Palenzuela 1710.09432

Damour & Esposito Farese 1993, 1996

⚫ Generates scalar GWs in stellar collape

Novak+ 1990s, Gerosa et al 2016

⚫ Constrains massless ST theory!

�6 �4 �2 0 2 4 6�0

10�4

10�3

10�2

↵0

PSRJ0348+0432

PSR J1738+0333

Cassini

Runs

Massive ST theories⚫ Massive fields: short range!

constraints only valid up to

⚫ Quasi-monochromatic signals lasting months to centuries

US et al 1708.03651

⚫ Suitable for LIGO

⚫ Historic SNe!

� =h

mcm . 10�16 eV

Compact binaries⚫ BH binaries in ST theory: Constrained by no-hair theorems!

But: scalar radiation for non-trivial BCs or potentials

Berti et al 1304.2836, Healy et al 1112.3928

⚫ NS binaries in ST theory: Dynamical scalarization

Palenzuela 1310.4481

⚫ BH binaries in dyn.Chern-Simons theory

⚫ TODO: smoking guns; parametric models

Well-posedness questionable

Delsate et al 1407.6727

Pert.approach around GR

Scalar signal

Okounkouva et al 1705.07924

)

High-energy collisions of BHs

Motivation: TeV Gravity

⚫ Particle collisions may form BHs E.g. Dimopoulos & Landsberg ‘01, Giddings & Thomas ’01

⚫ Provide data for LHC event generators

⚫ Collide BHs in dimensions

⚫ Gravity other forces

⚫ Gravity not measured below . Diluted due to

Large extra dimensions Arkani-Hamed, Dimopoulos, Dvali ‘98

Extra dimensions with warp factor Randall & Sundrum ‘99

⇡ 10�39⇥

Cross section for BH formation

Loss of energy and any.momentum in GWs

D > 4

⇠ 0.1 mm

Does matter matter?⚫ Hoop conjecture kinetic energy triggers BH formation

⚫ Einstein + minimally coupled, massive complex scalar field

“Boson stars” Choptuik & Pretorius 0908.1780

⚫ BH formation threshold

⚫ Model point particle collision by BH collisions

⚫ Similar results for collisions of perfect fluid balls

Rezzolla & Takami 1209.6138, East & Pretorius 1312.4529

)

�thr

= 2.9± 10% ⇠ 1/3 �hoop

Grazing collisions in D=4⚫ Spins: aligned, zero, anti aligned US et al 1211.6114

⚫ : spin effects washed out as bscat, Erad v ! c

Scattering threshold in D=5⚫ Numerical stability still an issue…

Okawa, Nakao & Shibata 1105.3331

Head-on collisions from rest in D=4…10⚫ strongly suppresses in higher

Cook et al 1709.10514

Erad D

4 5 6 7 8 9 10

D

10-5

10-4

10-3

Era

d /

M

Data

Fit: a0 (2π)

β/ Γ(β), β = (D-a

1) / a

2

Fit: b0 2 π

β/ Γ(β), β = (D-b

1) / b

2

⚫ But: No suppression for high mass ratios!

likely due to new length scales in high

⚫ TODO: High velocity in

D Emparan et al 1302.6382

D > 4

Fundamental properties of BHs

Motivation: Fundamental BH properties⚫ Cosmic censorship Lehner & Pretorius ’10, Figueras, Kunesch, Tunyasuvunakool et al. ’16, ’17

⚫ Stability of AdS Bizon & Rostworowski ’11

⚫ Stability of Hairy BH solutions of

Herdeiro & Radu 1403.02757

Herdeiro et al 1603.02687 ???

Summary of main open tasks⚫ Simulate signature of ultra-light fields in BH waveforms

⚫ GW templates from Boson Stars and other ultra-compact objects

⚫ Smoking gun signatures and waveform catalogues for GW sources

in alternative theories of gravity

⚫ High-energy collisions of BHs in

⚫ Stability and dynamics of Hairy BHs

⚫ Numerical relativity in other areas

> D

Nonlinear cosmology

AdS/CFT

Critical phenomena without spherical symmetry

…