GENERAL RELATIVITY AND...

GENERAL RELATIVITY AND GRAVITATIONA Centennial Perspective

Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wavescience, mathematics, computational science, and the interface of gravitation and quantumphysics with this unique celebration of the centennial of Einstein’s discovery of generalrelativity.

Twelve comprehensive and in-depth reviews, written by a team of leading internationalexperts, together present an up-to-date overview of key topics at the frontiers of these areas,with particular emphasis on the significant developments of the last three decades. Inter-connections with other fields of research are also highlighted, making this an invaluableresource for both new and experienced researchers.

Commissioned by the International Society on General Relativity and Gravitation, andincluding accessible introductions to cutting-edge topics, ample references to originalresearch papers, and informative color figures, this is a definitive reference for researchersand graduate students in cosmology, relativity, and gravitational science.

Abhay Ashtekar (Editor in Chief) is the founding Director of the Institute for Grav-itation and the Cosmos, and holds the Eberly Chair in Physics, at The Pennsylvania StateUniversity. He is a Fellow of the AAAS and the APS, and a former President of theInternational Society for General Relativity and Gravitation.

Beverly K. Berger is a former Program Director for Gravitational Physics at the USNational Science Foundation. She is a Fellow of the APS, and was the founder of the APSTopical Group on Gravitation.

James Isenberg is a Professor of Mathematics at the University of Oregon and formerEisenbud Professor at the Mathematical Sciences Research Institute in Berkeley. He is aFellow of the APS.

Malcolm MacCallum is Emeritus Professor of Applied Mathematics at QueenMary University of London. He was the founding editor of Classical and Quantum Gravityand is a former President of the International Society for General Relativity and Gravitation.

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Cambridge University Press978-1-107-03731-1 - General Relativity and Gravitation: A Centennial PerspectiveEdited by Abhay Ashtekar (Editor in Chief), Beverly K. Berger, James Isenberg and Malcolm MaccallumFrontmatterMore information

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“Expansive in scope, detailed in presentation, and rich in source referencing, GeneralRelativity and Gravitation is an authoritative treatment of the tremendous impact thatgeneral relativity has had – in both theoretical and experimental arenas – one hundredyears after Einstein produced his ground-breaking theory. Experts and students alike willfind many things to like in this book!”

David Reitze,California Institute of Technology

“Einstein wrote that a theory is more impressive the greater the simplicity of its premises,the more different kinds of things it relates, and the more extended its area of applicability.Nowhere could that be better said than of his own theory of relativistic gravity – generalrelativity – a century after its birth. General relativity has become central both for thephysics of the very large – astrophysics and cosmology – and of the very small – quantumgravity. This volume reviews that achievement. The scope is broad, the editing able, thetopics well chosen, and the authors are all distinguished experts. Care has been taken tomake the exposition as accessible as possible. Both the diversity and the unity of a greathistoric achievement are on display here.”

James Hartle,University of California, Santa Barbara






GENERAL RELATIVITY ANDGRAVITATION

A Centennial Perspective

Edited by

ABHAY ASHTEKAR (EDITOR IN CHIEF)The Pennsylvania State University

BEVERLY K. BERGERInternational Society on Relativity and Gravitation

JAMES ISENBERGUniversity of Oregon

MALCOLM MACCALLUMQueen Mary University of London






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It furthers the University’s mission by disseminating knowledge in the pursuit ofeducation, learning and research at the highest international levels of excellence.

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© Cambridge University Press 2015

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the written

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First published 2015

Printed in the United States of America by Sheridan Books, Inc.

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ISBN 978-1-107-03731-1 Hardback

Cambridge University Press has no responsibility for the persistence or accuracy ofURLs for external or third-party internet websites referred to in this publication,

and does not guarantee that any content on such websites is, or will remain,accurate or appropriate.






Contents

Preface page xiiiList of contributors xvList of figures xixList of tables xxii

Part One Einstein’s Triumph 1

Part One: Introduction 3

1 100 Years of General Relativity 10george f. r . ellis1.1 The study of dynamic geometry 11

1.1.1 Technical developments 121.1.2 Exact theorems and global structure 161.1.3 Singularity theorems 181.1.4 Conclusion 19

1.2 The Schwarzschild solution and the solar system 201.2.1 The Schwarzschild exterior solution 201.2.2 Effects on particles 211.2.3 Solar system tests of general relativity 211.2.4 Reissner–Nordstrom, Kottler, and Kerr solutions 221.2.5 Maximal extension of the Schwarzschild solution 221.2.6 Conclusion 25

1.3 Gravitational collapse and black holes 261.3.1 Spherically symmetric matter models 261.3.2 Causal diagrams 261.3.3 Accretion disks and domains 281.3.4 Powerhouses in astrophysics 291.3.5 Conclusion 29

1.4 Cosmology and structure formation 291.4.1 FLRW models and the Hot Big Bang 30






vi Contents

1.4.2 More general dynamics: inflation 331.4.3 Perturbed FLRW models and the growth of structure 341.4.4 The Standard Model of cosmology 351.4.5 More general geometries: LTB and Bianchi models 351.4.6 Cosmological success and puzzles 36

1.5 Gravitational lensing and dark matter 371.5.1 Calculating lensing 371.5.2 Strong lensing 381.5.3 Weak lensing 391.5.4 Microlensing 391.5.5 Conclusion 39

1.6 Gravitational waves 401.6.1 Weak-field formulation 401.6.2 Exact gravitational waves 411.6.3 Asymptotic flatness and gravitational radiation 411.6.4 Emission 421.6.5 Gravitational wave detection 421.6.6 Conclusion 43

1.7 Generalisations 44

2 Was Einstein Right? A Centenary Assessment 49clifford m. will2.1 Introduction 492.2 The foundations of gravitation theory 51

2.2.1 The Einstein equivalence principle 512.2.2 Metric theories of gravity and the strong equivalence principle 59

2.3 The parametrized post-Newtonian formalism 612.4 Competing theories of gravity 63

2.4.1 General relativity 642.4.2 Scalar–tensor theories 652.4.3 f (R) theories 672.4.4 Vector–tensor theories 682.4.5 Tensor–vector–scalar (TeVeS) theories 692.4.6 Other theories 70

2.5 Tests of post-Newtonian gravity 702.5.1 Tests of the parameter γ 702.5.2 The perihelion shift of Mercury 732.5.3 Tests of the strong equivalence principle 742.5.4 The search for gravitomagnetism 78

2.6 Binary-pulsar tests of gravitational theory 802.6.1 The binary pulsar and general relativity 812.6.2 A zoo of binary pulsars 84






Contents vii

2.6.3 Binary pulsars and alternative theories 872.7 Testing general relativity in its second century 88

2.7.1 Gravitational-wave tests 882.7.2 Strong-field tests 91

2.8 Conclusions 92

3 Relativistic Astrophysics 973.1 Introduction 97john friedman

3.1.1 Relativistic stars 1003.2 Gravitational lensing 118peter schneider

3.2.1 Introduction 1183.2.2 Basic theory 1193.2.3 Strong lensing by galaxies 1213.2.4 Galactic microlensing 1253.2.5 Weak gravitational lensing 1263.2.6 Natural telescopes 1313.2.7 Concluding remarks 131

3.3 Observational evidence for black holes 133ramesh narayan and jeffrey e. mcclintock

3.3.1 Historical introduction 1333.3.2 Supermassive black holes 1353.3.3 Stellar-mass black holes 1383.3.4 Physics of astrophysical black holes 1423.3.5 Conclusion 145

3.4 Gamma-ray bursts 148peter meszaros and martin j. rees

3.4.1 Historical overview and basic concepts 1483.4.2 CGRO results and basic models 1503.4.3 Beppo-SAX and HETE-2 results and issues 1523.4.4 Bursts in the Swift era 1533.4.5 Bursts at energies above GeV: Fermi and beyond 1573.4.6 GRBs in non-photonic channels? 158

4 Cosmology 1624.1 Introduction 162david wands and roy maartens

4.1.1 The Hot Big Bang 1634.1.2 Dark energy 1664.1.3 Inhomogeneous geometry and inflation 1674.1.4 Mapping the matter distribution on the past light cone 170






viii Contents

4.1.5 Outlook: general relativity and cosmology 1734.2 Inflationary cosmology 175misao sasaki

4.2.1 Introduction 1754.2.2 Inflation 1794.2.3 Cosmological perturbations from inflation 1844.2.4 Tensor perturbation 1864.2.5 Deviations from Gaussianity 1874.2.6 δN formalism 1894.2.7 Summary 193

4.3 Precision cosmology 195ei ichiro komatsu

4.3.1 Introduction 1954.3.2 Spectral distortions 1964.3.3 Temperature anisotropy due to our local motion 1984.3.4 Primordial temperature anisotropy: scalar modes 2004.3.5 Polarization: scalar modes 2094.3.6 Tensor modes 215

4.4 Beyond the standard model 221malcolm a. h. maccallum

4.4.1 Motivations and possible directions 2214.4.2 Spatially-homogeneous models 2244.4.3 Globally inhomogeneous models 2264.4.4 Cumulative effects of small-scale inhomogeneity 227

Part Two New Window on the Universe: Gravitational Waves 233

Part Two: Introduction 235

5 Receiving Gravitational Waves 242beverly k. berger, karsten danzmann, gabriela gonzalez,andrea lommen, guido mueller, albrecht rudiger andwilliam joseph weber5.1 Introduction 2425.2 The basic detection scheme 2445.3 Ground-based detectors 247

5.3.1 Advanced ground-based detectors 2495.3.2 The future of ground-based gravitational wave detectors 262

5.4 Space-based gravitational wave detectors 2655.4.1 Introduction 2655.4.2 Interferometry over millions of kilometers 2675.4.3 Achieving free-fall at a level below femto-g 2685.4.4 Prospects for a space-based mission 271






Contents ix

5.5 Pulsar timing 2725.5.1 Introduction 2725.5.2 Radio telescopes 2725.5.3 Detection principle 2735.5.4 Data analysis 2765.5.5 When will pulsar timing detect gravitational waves? 2785.5.6 Concluding remarks on pulsar timing 280

5.6 Summary 280

6 Sources of Gravitational Waves: Theory and Observations 287alessandra buonanno and b. s . sathyaprakash6.1 Historical perspective 2876.2 Analytical approximation methods 289

6.2.1 Post-Newtonian formalism 2926.2.2 Perturbation theory and gravitational self force 3006.2.3 The effective-one-body formalism 304

6.3 Compact-object binaries 3106.3.1 Frequency–mass diagram 3106.3.2 Zoo of compact-object binaries 3116.3.3 Interface between theory and observations 3156.3.4 Results from LIGO and Virgo 3186.3.5 Science targets and challenges 319

6.4 Isolated compact objects 3246.4.1 A menagerie of neutron-star sources 3246.4.2 Results from LIGO and Virgo 3276.4.3 Science targets and challenges 329

6.5 Gravitational radiation from the early Universe 3316.5.1 Primordial sources and expected strengths 3316.5.2 Results from LIGO and Virgo 3326.5.3 Science targets and challenges 333

Part Three Gravity is Geometry, after all 347

Part Three: Introduction 349

7 Probing Strong-Field Gravity Through Numerical Simulations 361matthew w. choptuik , luis lehner and frans pretorius7.1 Historical perspective 3627.2 Numerical relativity: current state of the art 365

7.2.1 Mathematical formalism 3657.2.2 Numerical methods 368

7.3 Strong-field gravity 3697.3.1 Critical phenomena in gravitational collapse 3697.3.2 Binary black hole mergers 377






x Contents

7.3.3 Black hole–neutron star/binary neutron star mergers 3827.3.4 Gravitational collapse to a neutron star or black hole 3867.3.5 Ultra-relativistic collisions 3887.3.6 Gravity in d �= 4 3927.3.7 Singularities 3977.3.8 Miscellaneous 398

7.4 Unsolved problems 401

8 Initial Data and the Einstein Constraint Equations 412gregory j. galloway, pengzi miao and richard schoen8.1 Introduction 4128.2 The Einstein constraint equations 413

8.2.1 The conformal method 4148.2.2 The asymptotically flat case 418

8.3 Quasi-local mass 4238.3.1 Quasi-local mass via Hamilton–Jacobi approach 4258.3.2 Hawking mass 4308.3.3 Bartnik mass 432

8.4 Marginally outer trapped surfaces 4338.4.1 Basic definitions 4348.4.2 Stability of MOTSs 4358.4.3 An existence result for MOTSs 4368.4.4 Black hole topology 4378.4.5 The topology of initial data sets 4398.4.6 MOTS and the spacetime positive mass theorem 442

9 Global Behavior of Solutions to Einstein’s Equations 4499.1 Introduction 449james isenberg9.2 The Cauchy problem in General Relativity 452stefanos aretakis and igor rodnianski

9.2.1 Introduction 4529.2.2 Well-posedness of the Einstein equations 4579.2.3 Stability problems in General Relativity 4669.2.4 Large-data regimes 472

9.3 Convergence and stability issues in mathematical cosmology 480vincent moncrief

9.3.1 Introduction 4809.3.2 Yamabe classification 4839.3.3 Hamiltonian reduction 4849.3.4 The σ constant and its cosmological significance 4869.3.5 Stability results 4879.3.6 An integral equation for spacetime curvature 490






Contents xi

Part Four Beyond Einstein 499

Part Four: Introduction 501

10 Quantum Fields in Curved Spacetime 513stefan hollands and robert m. wald10.1 The nature of quantum field theory in curved spacetime 51310.2 Free quantum fields 519

10.2.1 Formulation of linear QFTCS via the algebraic approach(without nonlinear observables) 519

10.2.2 Applications: Unruh effect, de Sitter space, Hawking effect,inflationary perturbations 528

10.3 Beyond linear quantum fields 54210.3.1 Construction of nonlinear observables for a free quantum

scalar field 54210.3.2 Time ordered products 54410.3.3 Interacting fields 546

11 From General Relativity to Quantum Gravity 553abhay ashtekar, martin reuter and carlo rovelli11.1 Introduction 55311.2 Frameworks 555

11.2.1 Asymptotic Safety 55611.2.2 Hamiltonian theory and quantum geometry 56711.2.3 Covariant loop gravity: spinfoams 577

11.3 Applications 58411.3.1 The very early universe 58511.3.2 Black holes 59211.3.3 n-point functions in a diffeomorphism invariant theory 597

11.4 Discussion 60011.4.1 Summary 60011.4.2 Outlook 602

12 Quantum Gravity via Supersymmetry and Holography 612henriette elvang and gary t. horowitz12.1 Gravity in D dimensions 614

12.1.1 Kaluza–Klein theory 61512.1.2 Black strings 61612.1.3 Asymptotically flat black holes in D = 5 vacuum gravity 61912.1.4 Asymptotically flat black holes in D > 5 vacuum gravity 623

12.2 Supergravity 62512.2.1 Supersymmetry 62512.2.2 Supergravity 62712.2.3 Charged black holes, BPS bounds, and Killing spinors 630






xii Contents

12.2.4 Perturbative quantum gravity 63312.3 String theory 636

12.3.1 Perturbative string theory 63612.3.2 Nonperturbative aspects of string theory

and quantum black holes 64112.4 Holography and gauge/gravity duality 647

12.4.1 Holography 64712.4.2 Gauge/gravity duality 64812.4.3 Applications 654

12.5 Conclusion 658

Index 667






Preface

The discovery of general relativity by Albert Einstein 100 years ago was quickly recognizedas a supreme triumph of the human intellect. To paraphrase Hermann Weyl, wider expansesand greater depths were suddenly exposed to the searching eye of knowledge, regions ofwhich there was not even an inkling. For 8 years, Einstein had been consumed by thetension between Newtonian gravity and the spacetime structure of special relativity. Atfirst no one had any appreciation for his passion. Indeed, “as an older friend,” Max Planckadvised him against this pursuit, “for, in the first place you will not succeed, and evenif you succeed, no one will believe you.” Fortunately Einstein persisted and discovered atheory that represents an unprecedented combination of mathematical elegance, conceptualdepth and observational success. For over 25 centuries, spacetime had been a stage onwhich the dynamics of matter unfolded. Suddenly the stage joined the troupe of actors. Asdecades passed, new aspects of this revolutionary paradigm continued to emerge. It wasfound that the entire universe is undergoing an expansion. Spacetime regions can get sowarped that even light can be trapped in them. Ripples of spacetime curvature can carrydetailed imprints of cosmic explosions in the distant reaches of the universe. A centuryhas now passed since Einstein’s discovery and yet every researcher who studies generalrelativity in a serious manner continues to be enchanted by its magic.

This volume was commissioned by the International Society on General Relativity andGravitation to celebrate a century of successive triumphs of general relativity as it expandedits scientific reach. Through its 12 Chapters, divided into four Parts, the volume takes usthrough this voyage, highlighting the advances that have occurred during the last threedecades or so, roughly since the publication of the 1979 volumes celebrating the cen-tennial of Einstein’s birth. During this period, general relativity and gravitational sciencehave moved steadily toward the center of physics, astrophysics and cosmology and havealso contributed to major advances in geometric analysis, computational science, quantumphysics and several areas of technology. The next two decades should be even more excitingas new observations from gravitational wave detectors and astronomical missions openunforeseen vistas in our understanding of the cosmos.

Beginning researchers should be able to use this volume as an introduction to the entirefield. More advanced researchers should be able to use individual Chapters, especially






xiv Preface

the Chapters that are outside the area of their immediate expertise, as brief overviews ofthe current status of those subjects. Since the scope of gravitational science has widenedconsiderably in recent years, the volume should be useful not only to specialists in generalrelativity but also to researchers in related areas, especially astrophysics, cosmology, com-putational science, high energy physics, quantum field theory and geometric analysis. Thedetailed introductions to each of the four Parts should help provide a global perspective ondevelopments in individual areas. They summarize the main advances and offer a shorttour of the more detailed material that can be found in the Chapters that follow. Theintroductions also contain illustrative examples of outstanding important open issues, andoutline important developments that could not be included in individual Chapters where theauthors had the difficult task of covering many developments in a limited space. Each ofthe four editors was primarily responsible for one of the four Parts of the volume, oversawrevisions, and lightly edited the material to enhance synergy among different Chapters inthat Part. In addition, the four editors jointly wrote the introductions to all four Parts.

We are fortunate that so many leading researchers not only agreed to contribute butprepared their Chapters with great care and cheerfully undertook revisions. We are grate-ful to them for this collaboration. As is clear from the acknowledgements in individualChapters, many authors sought comments from experts prior to submission. In addition,the editors requested between two and six external reviews for each Chapter. These reportsprovided excellent, detailed feedback which led to considerable improvements and a betteroverall balance. The quality of the final product owes a great deal to the seriousness withwhich the referees undertook their job. For this, we would like to express our deepestappreciation to Ivan Agullo, Lars Andersson, Nils Andersson, Fernando Barbero, EugenioBianchi, Sukanta Bose, Robert Brandenberger, Bernd Bruegmann, Piotr Chrusciel, MihalisDafermos, Ruth Durrer, Pedro Ferreira, Chris Fewster, Larry Ford, Klaus Fredenhagen,David Garfinkle, Ted Jacobson, George (Mac) Keiser, Alok Laddha, Roy Maartens, DavidMcClelland, Sharon Morsink, Maria Alessandra Papa, Roberto Percacci, Daniel Pollack,Hans Ringstrom, Peter Saulson, Kelly Stelle, Iva Stavrov, and Madhavan Varadarajan.Finally, we would like to thank our CUP Editor, Simon Capelin, for his constant supportand efficient help throughout this project.

Abhay Ashtekar (Editor in Chief)Beverly K. Berger

James IsenbergMalcolm A. H. MacCallum






Contributors

Stefanos AretakisInstitute for Advanced Study, Princeton, NJ 08540, USA and Princeton University,Department of Mathematics, Princeton, NJ 08544, USA

Abhay AshtekarInstitute for Gravitation & the Cosmos and Physics Department, The Pennsylvania StateUniversity, University Park, PA 16802-6300, USA

Beverly K. Berger2131 Chateau PL, Livermore, CA 94550, USA

Alessandra BuonannoMax Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476Potsdam-Golm, Germany

Matthew W. ChoptuikDepartment of Physics and Astronomy, University of British Columbia, Vancouver, BC,Canada V6T 1Z

Karsten DanzmannMax Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167Hannover, Germany

George F. R. EllisDepartment of Mathematics and Applied Mathematics, University of Cape Town,Rondebosch 7701, South Africa

Henriette ElvangDepartment of Physics, University of Michigan, Ann Arbor, MI 48109, USA






xvi List of contributors

John FriedmanDepartment of Physics, University of Wisconsin–Milwaukee, Milwaukee, WI 53211, USA

Gregory J. GallowayDepartment of Mathematics, University of Miami, Coral Gables, FL 33146, USA

Gabriela GonzalezDepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA70803, USA

Stefan HollandsUniversitat Leipzig, Institut fur Theoretische Physik, D-04103 Leipzig, Germany

Gary T. HorowitzDepartment of Physics, UCSB, Santa Barbara, CA, 93106, USA

James IsenbergDepartment of Mathematics, Fenton Hall, University of Oregon, Eugene, OR 97403-1222,USA

Eiichiro KomatsuMax-Planck-Institut fur Astrophysik, D-85741 Garching, Germany

Luis LehnerPerimeter Institute, Ontario, Canada N2L, 2Y5

Andrea LommenDepartment of Physics and Astronomy, Franklin & Marshall College, Lancaster, PA17604-3003, USA

Roy MaartensPhysics Department, University of the Western Cape, Cape Town 7535, South Africa andInstitute of Cosmology & Gravitation, University of Portsmouth, Portsmouth PO1 3FX,UK

Malcolm A. H. MacCallumSchool of Mathematical Sciences, Queen Mary University of London, Mile End Road,London E1 4NS, UK

Jeffrey E. McClintockHarvard Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA






List of contributors xvii

Peter MeszarosDepartment of Astronomy and Astrophysics, Department of Physics, The PennsylvaniaState University, PA 16802, USA

Pengzi MiaoDepartment of Mathematics, University of Miami, Coral Gables, FL 33146, USA

Vincent MoncriefDepartment of Physics, Yale University, New Haven, CT 06520-8120, USA

Guido MuellerDepartment of Physics, University of Florida, Gainesville, FL 32611, USA

Ramesh NarayanHarvard Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA

Frans PretoriusDepartment of Physics, Princeton University, Princeton, NJ 08544, USA

Martin J. ReesInstitute of Astronomy, University of Cambridge, Cambridge CB3 0HA, UK

Martin ReuterInstitute of Physics, University of Mainz, D-55099 Mainz, Germany

Igor RodnianskiMassachusetts Institute of Technology, Department of Mathematics, Cambridge, MA02139, United States and Princeton University, Department of Mathematics, Princeton, NJ08544, USA

Carlo RovelliCentre de Physique Theorique, Universite de Marseille, F-13288 Marseille, France

Albrecht RudigerAlbert Einstein Institute, D-30167 Hannover, Germany

Misao SasakiYukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

B. S. SathyaprakashSchool of Physics and Astronomy, Cardiff University, Cardiff CF24 3YB, UK






xviii List of contributors

Peter SchneiderArgelander-Institut fur Astronomie, D-53121 Bonn, Germany

Richard SchoenDepartment of Mathematics University of California, Irvine, Irvine, CA 92697-3875, USA

Robert M. WaldEnrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL60637, USA

David WandsInstitute of Cosmology & Gravitation, University of Portsmouth, Portsmouth, PO1 3FX,UK

William Joseph WeberDepartment of Physics, University of Trento, 38123 Povo, Trento, Italy and TrentoInstitute for Fundamental Physics and Application/INFN, 38123 Povo, Trento, Italy

Clifford M. WillDepartment of Physics, University of Florida, Gainesville, FL 32611, USA






List of figures

1.1 The Eddington–Finkelstein extension of the Schwarschild solution page 241.2 The Kruskal maximal extension of the Schwarzschild vacuum solution 251.3 Collapse to a black hole 271.4 Penrose diagram of collapse to a black hole 282.1 Selected tests of the weak equivalence principle 532.2 Selected tests of local Lorentz invariance 552.3 Selected tests of local position invariance 572.4 Measurements of (1 + γ )/2 from light deflection and time delay 722.5 Constraints on B1913+16 component masses assuming general relativity 832.6 Plot of the cumulative shift of the periastron time from 1975–2005 842.7 Constraints on masses of J0737–3039A,B from general relativity 852.8 Six polarization modes permitted in any metric theory 893.1 Constraints from causality and a > 2.0 M� maximum mass on parametrized

equations of state 1053.2 Critical angular velocity vs. dimensionless central energy density for neutral

modes of polytropes 1093.3 Critical angular velocity for the onset of the r-mode instability as a function of

temperature 1103.4 The arc system of the cluster of galaxies A2218 1193.5 Geometry of a gravitational lens system 1203.6 Eight strong lens systems 1223.7 A modern radio image of Cyg A 1343.8 Orbital tracks of 8 bright stars at the center of our Galaxy 1363.9 Observed correlations of supermassive black hole mass with host

galaxy bulge infrared luminosity and velocity dispersion 1383.10 Sketches of 21 black hole binaries 1393.11 A sequence of radio images of GRS 1915+105 from 1994 1433.12 The “fundamental plane of black hole activity” 1443.13 Jet power versus black hole spin and RISCO/Rg 1453.14 Gamma-ray light curves from the BATSE instrument 1493.15 Schematic GRB jet from a collapsing star. 1513.16 X-ray light curve of GRB060428A observed by the Swift XRT 154






xx List of figures

3.17 Spectra of GRB090926A 1584.1 Horizon problem 1774.2 The solution to the horizon problem 1784.3 The Hubble radius and comoving length scale in inflation, and the number

of e-folds 1834.4 The energy density configuration in the multi-field case 1894.5 Three different types of δN 1904.6 Definition of nonlinear δN 1914.7 Power spectrum of temperature anisotropy of the CMB 2074.8 Power spectrum of lensing potential from the Planck 15.5-month

temperature data 2094.9 Average images of temperature and polarization data 2104.10 Definition of Stokes Q and U 2124.11 Cross power spectrum of temperature and E-mode polarization 2134.12 Power spectrum of E-mode polarization anisotropy 2144.13 Detection of lensing-induced B-mode polarization 2164.14 How gravitational waves stretch and contract space 2174.15 Power spectra of B-mode polarization of the CMB 2185.1 Sensitivities of all first-generation ground-based detectors. 2485.2 Typical sensitivity curve for advanced detectors 2505.3 Schematic of Advanced LIGO laser and input optics 2545.4 Schematic of Advanced LIGO main interferometer and output optics 2565.5 The Virgo superattenuator 2605.6 The Advanced LIGO suspension system 2615.7 eLISA sensitivity 2665.8 Scientific payload for LISA-like mission 2665.9 Schematic of LISA Pathfinder payload 2705.10 Pulsar timing residuals 2745.11 Pulsar response to linearly polarized gravitational wave 2755.12 Detection probability versus time 2796.1 Range of validity of analytical and numerical methods 2916.2 Schematic diagram of an inspiraling binary 2936.3 The real and effective descriptions in the EOB formalism 3066.4 Gravitational waveform and frequencies from inspiral, plunge, merger

and ringdown 3096.5 Frequency–mass diagram for equal-mass compact binaries 3116.6 Sources of gravitational waves for ground-based detectors 3146.7 Sources of gravitational waves for space-borne detectors 3146.8 State-of-the-art comparison between EOB and NR waveforms 3177.1 Scalar field critical collapse solution 3737.2 Gravitational wave emission from the simulation of an equal mass

binary black hole merger 3797.3 Recoil velocities from equal-mass, spinning binary black hole merger

simulations 3807.4 Interaction of a binary black hole with a magnetized accretion disk 381






List of figures xxi

7.5 Gravitational wave emission from binary neutron star merger simulations 3837.6 Tidal disruption of a neutron star merging with a black hole 3857.7 Simulation of stellar collapse to a black hole 3877.8 Evolution of an unstable black string 3937.9 Shock wave collision and perturbed black hole in AdS 3967.10 Turbulence in black branes and relativistic fluids 3979.1 The two surface S0 4549.2 The section Su0,v0 of the double null foliation 455

10.1 Conformal diagram for de Sitter spacetime and values of the invariant Z(x, y) 53110.2 Conformal diagram for de Sitter spacetime and the static chart 53310.3 Conformal diagram of an eternal black hole 53410.4 Conformal diagram of collapsing star spacetime 53610.5 A wave-front set 55111.1 Renormalization group flows 56311.2 2-complex terminology 57811.3 Continuum versus classical limit 58211.4 Classical versus LQC dynamics of FLRW models 58611.5 Quantum horizon geometry 59411.6 Transition amplitude 59812.1 Kaluza–Klein black hole horizons 61712.2 Phase diagram for Kaluza–Klein black holes 61912.3 Phase diagram for asymptotically flat black holes 62112.4 A one-loop string diagram 63912.5 Weak coupling limits of M-theory 643






List of tables

2.1 Bounds on cosmological variation of fundamental constants ofnon-gravitational physics page 59

2.2 PPN parameters and their significance 632.3 Metric theories and their PPN parameter values 652.4 Current limits on the PPN parameters 772.5 Constancy of the gravitational constant 782.6 Parameters of the binary pulsar B1913+16 813.1 Masses and spins, determined via the continuum-fitting method, for a selected

sample of seven black holes 1404.1 The six cosmological parameters of the standard flat �CDM model 2086.1 State-of-the-art of PN calculations for compact binaries with comparable

masses 3006.2 State-of-the-art of PN calculations in BH perturbation theory 301






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