DOCSLIB.ORG

Applications of Perturbation Theory in Black Hole Physics Paolo

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Applications of Perturbation Theory in Black Hole Physics Paolo UNIVERSITA` DEGLI STUDI DI CAGLIARI Facolt`adi Scienze Matematiche, Fisiche e Naturali Applications of perturbation theory in black hole physics Paolo Pani A thesis submitted for the degree of Doctor of Philosophy Supervisor: Prof. Mariano Cadoni January 2010 Abstract Black holes have many faces. Arguably, they are the most interesting objects in theoretical physics, revealing the elusive connection between gravity and quantum mechanics. Within the gauge/string duality they provide useful insights on strongly coupled quantum field theories and on quantum gravity. Furthermore, probing the strong curvature regime of any grav- ity theory, black holes carry the imprint of possible strong curvature corrections to General Relativity. Finally, beside their unique theoretical properties, several experimental evidences suggest that astrophysical black holes exist in nature and they are believed to be very com- mon objects in the universe. In this dissertation we discuss several applications of linear perturbation theory in black hole physics. As applications in theoretical physics, we study perturbations of dilatonic black holes in Einstein-Maxwell theory and the holographic prop- erties of the dual field theory via the Anti de Sitter/Condensed Matter duality. Furthermore we discuss a method to compute long-lived quasinormal modes of Schwarzschild-Anti de Sit- ter black holes and we study vortex black hole solutions in three dimensional Anti de Sitter gravity. As applications in astrophysics, we discuss how the characteristic oscillations of black holes in string-inspired theories of gravity can provide observable signatures of deviations from General Relativity. We study two well-motivated effective theories: Dynamical Chern-Simons gravity and Einstein-Dilatonic-Gauss-Bonnet gravity. We conclude by discussing the black hole paradigm. Motivated by the lacking of a definitive answer on the existence of astrophysi- cal black holes, we study some viable alternatives, generally called “black hole mimickers”. We focus on two representative cases: static thin-shell gravastars and superspinars. We discuss their stability, gravitational-wave signature and viability as astrophysical objects. KEY-WORDS: Black holes; Perturbation theory; AdS/CFT correspondence; Holography; Modified gravity; Effective theories; Gravitational waves; Quasinormal modes; Black hole mimickers. a Giu `equalche cosa che hai fatto, suppongo. Acknowledgements I wish to thank the University of Cagliari and the Italian National Institute of Nuclear Physics (INFN) for financial and logistical support and the Master and Back foundation programme of Regione Sardegna for a grant. This work has been also partially founded by FCT - Portugal through project PTDC/FIS/098032/2008. I warmly thank my supervisor, Mariano Cadoni, for his guidance, for all the physics he taught me and for the possibility he gave me to find my way in gravitational physics. I am also extremely grateful to Vitor Cardoso. It is a pleasure and an honor to work with him, being always conscious that I will have something important to learn. A special thanks goes to Emanuele Berti. Although we have not met (yet!), the useful discussions we had, and his irreplaceable contributions to our works, certainly made me a better physicist. During these years, I had the pleasure to work with Enrico Barausse, Yanbei Chen, Giuseppe D’Appollonio, Leonardo Gualtieri, Carlos Molina, Richard Norte and Matteo Serra. Many parts of this work are the outcome of various fruitful collaborations with them. I would like to thank my gravity-group mates in Cagliari: Maurizio Melis and Cristina Monni, and those I met in Lisbon: Mariam Bouhmadi, Jordi Casanellas, Magdalena Lemos, Andrea Nerozzi, Jorge Rocha and Helvi Witek. I hope we will have many other interesting discussions in future. I cannot express my gratitude enough to my parents Francesco and Rosanna and to my sister Carly, for their constant support, to the rest of my family, especially to my grandmothers and to my aunt Lella, who helped me in correcting this thesis, and to my family-in-law: Albi, Dianella, Fra and Gino. To my long, long-dated friends, Ale, Alessandra, Beccio, Fede, Giorgio, Marzia, Matte, Pierma, Ricca, Save, Valeria(s). They share the misfortune to be the people who know me better and, in spite of this, they will always support me with their love. Se’ bon a’ sutt! I would like to thank all the members of the Physics Department in Cagliari, who contribute to make it a wonderful place to work in. In particular my physics-class mates and friends, Francesco, Giamba, Nicola, Scrilly and Gary, the No-Trash Cougar. Although we took different paths and we are now spread around the world, we keep constantly nonsensing about physics and white weapons. In this difficult period, during which Italian Governments are degrading Public Education and Academic Research year by year, I cannot forget to express my gratitude to my high school Science professors: Maria Tonina Fancello, Guido Orr`u, Maria Clorinda Todde and Luigi Uras. If now I am physicist, this is also due to their early guidance. Last, as usual, comes Giu. Sharing the life with you, with your unconditional love, energy, peace of mind and happiness, makes me a better person. I love you. Contents Preface .......................................... xiii Introduction 1 I Black holes in Anti de Sitter space 7 1 Black holes and Anti de Sitter/Condensed Matter duality 9 1.1 A new approach to strongly coupled field theories . .......... 9 1.2 AdS/CFTcorrespondenceinanutshell. ....... 11 1.3 Holographic properties of AdS black holes . ......... 13 2 Charged dilatonic black holes in AdS 21 2.1 Introduction.................................... 21 2.2 Instability of AdS-RN black holes in Einstein-Maxwell-dilaton gravity . 23 2.3 Numerical solutions of the field equations . ......... 28 2.4 Thezerotemperaturelimit . 30 2.5 Holographic properties of the new black hole solution . ............. 33 2.6 Conclusions ..................................... 40 2.7 Appendix: Scalar hairs in the probe limit. Schwarzschild-AdS background . 42 3 Phase transitions and holography of dyonic black holes in AdS 45 3.1 Introduction.................................... 45 3.2 Instability of dyonic AdS-RN black holes . ......... 46 3.3 Dyonic black holes with scalar hairs . ....... 47 3.4 Holographic properties of DDBHs . ...... 52 3.5 Purelymagneticblackholes . ..... 55 3.6 Discussion...................................... 59 4 Breit-Wigner resonances and the quasinormal modes of AdS black holes 61 4.1 Introduction.................................... 61 4.2 Quasi-bound states in SAdS black holes . ....... 62 4.3 Long-lived modes in the eikonal limit . ........ 67 4.4 Conclusionsandoutlook . 68 Table of Contents 5 Scalar hairs and exact vortex solutions in 3D AdS gravity 69 5.1 Introduction.................................... 69 5.2 Dynamics of a complex scalar field in 3D AdS spacetime . ......... 71 5.3 Scalarhairs ..................................... 72 5.4 Linearformofthefieldequations . ...... 73 5.5 Black hole solutions with real scalar hairs . .......... 74 5.6 Vortexsolutions ................................. 76 5.7 Conclusions ..................................... 78 II Signatures of black holes beyond General Relativity 81 6 Black holes in alternative theories of gravity 83 6.1 Do we really need some alternative to General Relativity?............ 83 6.2 Thehairyblackholeszoo .. .. .. .. .. .. .. .. 85 6.3 No-hairtheoremtests ............................. 86 6.4 Alternative theories of gravity. Two cases studies. ............. 87 7 Gravitational signature of black holes in Dynamical Chern-Simons gravity 93 7.1 Introduction.................................... 93 7.2 Perturbation equations and dynamical stability . ............ 96 7.3 Numericalapproach ............................... 97 7.4 Numericalresults................................ 101 7.5 Discriminating the QNMs: no-hair tests . ........107 7.6 Conclusions ..................................... 109 7.7 Appendix: Ghost-like instabilities for β < 0 ....................110 8 Black holes in Einstein-Dilatonic-Gauss-Bonnet gravity 113 8.1 Introduction.................................... 114 8.2 Spherically symmetric BHs in Einstein-Dilaton-Gauss-Bonnet theory . 116 8.3 Linearstabilityanalysis . 118 8.4 Slowly rotating BHs in EDGB theory . 122 8.5 BHGeodesicsinEDGBtheory . 124 8.6 Discussion...................................... 134 8.7 Appendix: Linear stability analysis: axial perturbations .............135 8.8 Appendix: Slowly rotating Kerr black holes in the Hartle approximation . 137 III Black hole mimickers 139 9 Are really black holes out there? 141 10 Gravitational-wave signature of a thin-shell gravastar 145 10.1Introduction................................... 146 10.2 Equilibriummodel ............................... 147 10.3 Gravitational perturbations . ........149 10.4 NumericalResults ............................... 155 x Table of Contents 10.5 Gravitational perturbations by a point particle . .............161 10.6 Gravitational flux from gravastars and black holes . ............165 10.7 Conclusionsandoutlook . 171 10.8 Appendix: Perturbation equations and matching conditions ........... 172 10.9 Appendix: The continued fraction method . .........177 10.10Appendix: High-compactness limit . .........181 11 Gravitational instabilities of superspinars 183 11.1Introduction................................... 183 11.2 A simple model of superspinar in four dimensions . ...........185 11.3Perfectmirror
Load more

Recommended publications
  • Arxiv:0905.1355V2 [Gr-Qc] 4 Sep 2009 Edrt 1 O Ealdrve) Nti Otx,Re- Context, Been Has As This Collapse in Denoted Gravitational of Review)
    Can accretion disk properties distinguish gravastars from black holes? Tiberiu Harko∗ Department of Physics and Center for Theoretical and Computational Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong Zolt´an Kov´acs† Max-Planck-Institute f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany and Department of Experimental Physics, University of Szeged, D´om T´er 9, Szeged 6720, Hungary Francisco S. N. Lobo‡ Centro de F´ısica Te´orica e Computacional, Faculdade de Ciˆencias da Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal (Dated: September 4, 2009) Gravastars, hypothetic astrophysical objects, consisting of a dark energy condensate surrounded by a strongly correlated thin shell of anisotropic matter, have been proposed as an alternative to the standard black hole picture of general relativity. Observationally distinguishing between astrophysical black holes and gravastars is a major challenge for this latter theoretical model. This due to the fact that in static gravastars large stability regions (of the transition layer of these configurations) exist that are sufficiently close to the expected position of the event horizon, so that it would be difficult to distinguish the exterior geometry of gravastars from an astrophysical black hole. However, in the context of stationary and axially symmetrical geometries, a possibility of distinguishing gravastars from black holes is through the comparative study of thin accretion disks around rotating gravastars and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around slowly rotating gravastars, with all the metric tensor components estimated up to the second order in the angular velocity.
    [Show full text]
  • Quantum-Corrected Rotating Black Holes and Naked Singularities in (2 + 1) Dimensions
    PHYSICAL REVIEW D 99, 104023 (2019) Quantum-corrected rotating black holes and naked singularities in (2 + 1) dimensions † ‡ Marc Casals,1,2,* Alessandro Fabbri,3, Cristián Martínez,4, and Jorge Zanelli4,§ 1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, CEP 22290-180, Brazil 2School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland 3Departamento de Física Teórica and IFIC, Universidad de Valencia-CSIC, C. Dr. Moliner 50, 46100 Burjassot, Spain 4Centro de Estudios Científicos (CECs), Arturo Prat 514, Valdivia 5110466, Chile (Received 15 February 2019; published 13 May 2019) We analytically investigate the perturbative effects of a quantum conformally coupled scalar field on rotating (2 þ 1)-dimensional black holes and naked singularities. In both cases we obtain the quantum- backreacted metric analytically. In the black hole case, we explore the quantum corrections on different regions of relevance for a rotating black hole geometry. We find that the quantum effects lead to a growth of both the event horizon and the ergosphere, as well as to a reduction of the angular velocity compared to their corresponding unperturbed values. Quantum corrections also give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the naked singularity case, quantum effects lead to the formation of a horizon that hides the conical defect, thus turning it into a black hole. The fact that these effects occur not only for static but also for spinning geometries makes a strong case for the role of quantum mechanics as a cosmic censor in Nature.
    [Show full text]
  • Traversable Wormholes and Regenesis
    Traversable Wormholes and Regenesis The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Gao, Ping. 2019. Traversable Wormholes and Regenesis. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029626 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Traversable Wormholes and Regenesis A dissertation presented by Ping Gao to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts April 2019 c 2019 | Ping Gao All rights reserved. Dissertation Advisor: Daniel Louis Jafferis Ping Gao Traversable Wormholes and Regenesis Abstract In this dissertation we study a novel solution of traversable wormholes in the context of AdS/CFT. This type of traversable wormhole is the first such solution that has been shown to be embeddable in a UV complete theory of gravity. We discuss its property from points of view of both semiclassical gravity and general chaotic system. On gravity side, after turning on an interaction that couples the two boundaries of an eternal BTZ black hole, in chapter 2 we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation.
    [Show full text]
  • Light Rays, Singularities, and All That
    Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition .
    [Show full text]
  • Advanced Lectures on General Relativity
    Lecture notes prepared for the Solvay Doctoral School on Quantum Field Theory, Strings and Gravity. Lectures given in Brussels, October 2017. Advanced Lectures on General Relativity Lecturing & Proofreading: Geoffrey Compère Typesetting, layout & figures: Adrien Fiorucci Fonds National de la Recherche Scientifique (Belgium) Physique Théorique et Mathématique Université Libre de Bruxelles and International Solvay Institutes Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium Please email any question or correction to: [email protected] Abstract — These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as con- served quantities in theories of gravity; (2) Classical and holographic features of three-dimensional Einstein gravity; (3) Asymptotically flat spacetimes in 4 dimensions: BMS group and memory effects; (4) The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions. Table of contents 1 Surface charges in Gravitation ................................... 7 1.1 Introduction : general covariance and conserved stress tensor..............7 1.2 Generalized Noether theorem................................. 10 1.2.1 Gauge transformations and trivial currents..................... 10 1.2.2 Lower degree conservation laws........................... 11 1.2.3 Surface charges in generally covariant theories................... 13 1.3 Covariant phase space formalism............................... 14 1.3.1 Field fibration and symplectic structure....................... 14 1.3.2 Noether’s second theorem : an important lemma................. 17 Einstein’s gravity.................................... 18 Einstein-Maxwell electrodynamics.......................... 18 1.3.3 Fundamental theorem of the covariant phase space formalism.......... 20 Cartan’s magic formula...............................
    [Show full text]
  • Static Charged Fluid in (2+ 1)-Dimensions Admitting Conformal
    Accepted for publication in IJMPD STATIC CHARGED FLUID IN (2 + 1)-DIMENSIONS ADMITTING CONFORMAL KILLING VECTORS FAROOK RAHAMAN Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India [email protected] SAIBAL RAY Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata 700 010, West Bengal, India [email protected] INDRANI KARAR Department of Mathematics, Saroj Mohan Institute of Technology, Guptipara, West Bangal, India [email protected] HAFIZA ISMAT FATIMA Department of Mathematics, The University of Lahore, Lahore, Pakistan [email protected] SAIKAT BHOWMICK Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India [email protected] arXiv:1211.1228v3 [gr-qc] 24 Feb 2014 GOURAB KUMAR GHOSH Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India [email protected] Received Day Month Year Revised Day Month Year Communicated by Managing Editor New solutions for (2 + 1)-dimensional Einstein-Maxwell space-time are found for a static spherically symmetric charged fluid distribution with the additional condition of allowing conformal killing vectors (CKV). We discuss physical properties of the fluid parameters. Moreover, it is shown that the model actually represents two structures, namely (i) Gravastar as an alternative of black hole and (ii) Electromagnetic Mass model depending on the nature of the equation state of the fluid. Here the gravitational mass originates from electromagnetic field alone. The solutions are matched with the exterior region of the Ba˜nados-Teitelboim-Zanelli (BTZ) type isotropic static charged black hole as a 1 Accepted for publication in IJMPD 2 consequence of junction conditions. We have shown that the central charge density is dependent on the value of M0, the conserved mass of the BTZ black hole.
    [Show full text]
  • Linear Stability of Slowly Rotating Kerr Black Holes
    LINEAR STABILITY OF SLOWLY ROTATING KERR BLACK HOLES DIETRICH HAFNER,¨ PETER HINTZ, AND ANDRAS´ VASY Abstract. We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie in a fixed 7-dimensional space with a simple geometric interpretation. Our proof rests on a robust general framework, based on recent advances in microlocal analysis and non-elliptic Fredholm theory, for the analysis of resolvents of operators on asymptotically flat spaces. With the mode stability of the Schwarzschild metric as well as of certain scalar and 1-form wave operators on the Schwarzschild spacetime as an input, we establish the linear stability of slowly rotating Kerr black holes using perturbative arguments; in particular, our proof does not make any use of special algebraic properties of the Kerr metric. The heart of the paper is a detailed description of the resolvent of the linearization of a suitable hyperbolic gauge-fixed Einstein operator at low energies. As in previous work by the second and third authors on the nonlinear stability of cosmological black holes, constraint damping plays an important role. Here, it eliminates certain pathological generalized zero energy states; it also ensures that solutions of our hyperbolic formulation of the linearized Einstein equations have the stated asymptotics and decay for general initial data and forcing terms, which is a useful feature in nonlinear and numerical applications.
    [Show full text]
  • Table of Contents (Print)
    PHYSICAL REVIEW D PERIODICALS For editorial and subscription correspondence, Postmaster send address changes to: please see inside front cover (ISSN: 1550-7998) APS Subscription Services P.O. Box 41 Annapolis Junction, MD 20701 THIRD SERIES, VOLUME 101, NUMBER 10 CONTENTS D15 MAY 2020 The Table of Contents is a total listing of Parts A and B. Part A consists of articles 101501–104021, and Part B articles 104022–109903(E) PART A RAPID COMMUNICATIONS Faithful analytical effective-one-body waveform model for spin-aligned, moderately eccentric, coalescing black hole binaries (7 pages) ........................................................................................... 101501(R) Danilo Chiaramello and Alessandro Nagar ARTICLES Study of the ionization efficiency for nuclear recoils in pure crystals (10 pages) .............................................. 102001 Y. Sarkis, Alexis Aguilar-Arevalo, and Juan Carlos D’Olivo Observation of a potential future sensitivity limitation from ground motion at LIGO Hanford (12 pages) ................ 102002 J. Harms, E. L. Bonilla, M. W. Coughlin, J. Driggers, S. E. Dwyer, D. J. McManus, M. P. Ross, B. J. J. Slagmolen, and K. Venkateswara Efficient gravitational-wave glitch identification from environmental data through machine learning (12 pages) ......... 102003 Robert E. Colgan, K. Rainer Corley, Yenson Lau, Imre Bartos, John N. Wright, Zsuzsa Márka, and Szabolcs Márka Limits on the stochastic gravitational wave background and prospects for single-source detection with GRACE Follow-On (6 pages) ........................................................................................................ 102004 M. P. Ross, C. A. Hagedorn, E. A. Shaw, A. L. Lockwood, B. M. Iritani, J. G. Lee, K. Venkateswara, and J. H. Gundlach Analysis and visualization of the output mode-matching requirements for squeezing in Advanced LIGO and future gravitational wave detectors (14 pages) ............................................................................................
    [Show full text]
  • PHY390, the Kerr Metric and Black Holes
    PHY390, The Kerr Metric and Black Holes James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University April 1, 2021 Black Holes, Neutron Stars and Gravitational Radiation [email protected] James Lattimer PHY390, The Kerr Metric and Black Holes What Exactly is a Black Hole? Standard definition: A region of space from which nothing, not even light, can escape. I Where does the escape velocity equal the speed of light? r 2GMBH vesc = = c RSch This defines the Schwarzschild radius RSch to be 2GMBH M RSch = 2 ' 3 km c M I The event horizon marks the point of no return for any object. I A black hole is black because it absorbs everything incident on the event horizon and reflects nothing. I Black holes are hypothesized to form in three ways: I Gravitational collapse of a star I A high energy collision I Density fluctuations in the early universe I In general relativity, the black hole's mass is concentrated at the center in a singularity of infinite density. James Lattimer PHY390, The Kerr Metric and Black Holes John Michell and Black Holes The first reference is by the Anglican priest, John Michell (1724-1793), in a letter written to Henry Cavendish, of the Royal Society, in 1783. He reasoned, from observations of radiation pressure, that light, like mass, has inertia. If gravity affects light like its mass equivalent, light would be weakened. He argued that a Sun with 500 times its radius and the same density would be so massive that it's escape velocity would exceed light speed.
    [Show full text]
  • Holography of the BTZ Black Hole, Inside and out Arxiv:1307.7738V2
    UMD-PP-013-008 Holography of the BTZ Black Hole, Inside and Out Anton de la Fuente and Raman Sundrum Maryland Center for Fundamental Physics Department of Physics University of Maryland College Park, 20782 MD Abstract We propose a 1 + 1 dimensional CFT dual structure for quantum gravity and matter on the extended 2 + 1 dimensional BTZ black hole, realized as a quotient of the Poincaré patch of AdS3. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincaré patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon.
    [Show full text]
  • Conformal Field Theory and Black Hole Physics
    CONFORMAL FIELD THEORY AND BLACK HOLE PHYSICS Steve Sidhu Bachelor of Science, University of Northern British Columbia, 2009 A Thesis Submitted to the School of Graduate Studies of the University of Lethbridge in Partial Fulfilment of the Requirements for the Degree MASTER OF SCIENCE Department of Physics and Astronomy University of Lethbridge LETHBRIDGE, ALBERTA, CANADA c Steve Sidhu, 2012 Dedication To my parents, my sister, and Paige R. Ryan. iii Abstract This thesis reviews the use of 2-dimensional conformal field theory applied to gravity, specifically calculating Bekenstein-Hawking entropy of black holes in (2+1) dimen- sions. A brief review of general relativity, Conformal Field Theory, energy extraction from black holes, and black hole thermodynamics will be given. The Cardy formula, which calculates the entropy of a black hole from the AdS/CFT duality, will be shown to calculate the correct Bekenstein-Hawking entropy of the static and rotating BTZ black holes. The first law of black hole thermodynamics of the static, rotating, and charged-rotating BTZ black holes will be verified. iv Acknowledgements I would like to thank my supervisors Mark Walton and Saurya Das. I would also like to thank Ali Nassar and Ahmed Farag Ali for the many discussions, the Theo- retical Physics Group, and the entire Department of Physics and Astronomy at the University of Lethbridge. v Table of Contents Approval/Signature Page ii Dedication iii Abstract iv Acknowledgements v Table of Contents vi 1 Introduction 1 2 Einstein’s field equations and black hole solutions 7 2.1 Conventions and notations . 7 2.2 Einstein’s field equations .
    [Show full text]
  • Black Holes - No Need to Be Afraid! Transcript
    Black Holes - No need to be afraid! Transcript Date: Wednesday, 27 October 2010 - 12:00AM Location: Museum of London Gresham Lecture, Wednesday 27 October 2010 Black Holes – No need to be afraid! Professor Ian Morison Black Holes – do not deserve their bad press! Black holes seem to have a reputation for travelling through the galaxy “hovering up” stars and planets that stray into their path. It’s not like that. If our Sun were a black hole, we would continue to orbit just as we do now – we just would not have any heat or light. Even if a star were moving towards a massive black hole, it is far more likely to swing past – just like the fact very few comets hit the Sun but fly past to return again. So, if you are reassured, then perhaps we can consider…. What is a black Hole? If one projected a ball vertically from the equator of the Earth with increasing speed, there comes a point, when the speed reaches 11.2 km/sec, when the ball would not fall back to Earth but escape the Earth's gravitational pull. This is the Earth's escape velocity. If either the density of the Earth was greater (so its mass increases) or its radius smaller (or both) then the escape velocity would increase as Newton's formula for escape velocity shows: (0 is the escape velocity, M the mass of the object, r0 its radius and G the universal constant of gravitation.) If one naively used this formula into realms where relativistic formula would be needed, one could predict the mass and/or size of an object where the escape velocity would exceed the speed of light and thus nothing, not even light, could escape.
    [Show full text]