Evolution of black holes in anti-de sitter spacetime and the firewall controversy : doctoral thesis accepted by National Taiwan University, Taipei, Taiwan

This thesis focuses on the recent firewall controversy surrounding evaporating black holes, and shows that in the best understood example concerning electrically charged black holes with a flat event horizon in anti-de Sitter (AdS) spacetime, the firewall does not arise. The firewall, which surrounds a sufficiently old black hole, threatens to develop into a huge crisis since it could occur even when spacetime curvature is small, which contradicts general relativity. However, the end state for asymptotically flat black holes is ill-understood since their curvature becomes unbounded. This issue is avoided by working with flat charged black holes in AdS. The presence of electrical charge is crucial since black holes inevitably pick up charges throughout their long lifetime. These black holes always evolve toward extremal limit, and are then destroyed by quantum gravitational effects. This happens sooner than the time required to decode Hawking radiation so that the firewall never sets in, as conjectured by Harlow and Hayden. Motivated by the information loss paradox, the author also investigates the possibility that “monster” configurations might exist, with an arbitrarily large interior bounded by a finite surface area. Investigating such an object in AdS shows that in the best understood case, such an object -- much like a firewall -- cannot exist. Supervisor's Foreword I 8 Foreword II 10 Preface 12 Acknowledgments 15 Contents 17 Notations & Conventions 19 1 A Century of Black Hole Physics: From Classical Geometry to Hawking Radiation and the Firewall Controversy 21 1.1 The Mathematical Discovery of Black Holes 21 1.2 The Thermodynamics of Black Holes 29 1.3 Hawking Radiation: Black Holes Are not so Black 31 1.4 The Information Loss Paradox and Firewalls 36 1.5 There's Plenty of Room at the Bottom 46 1.6 Some Other Approaches to Resolve the Information Loss Paradox and Firewall Controversy 49 References 51 2 General Relativity: Subtle Is the Lord 56 2.1 What is General Relativity? 56 2.1.1 Differential Geometry in a Nutshell 57 2.1.2 The Einstein Field Equations 63 2.2 Some Subtleties of General Relativity 66 2.3 Is the Metric Just Another Field? 69 2.4 Equivalence Principle, Einstein's elevator, and All that 71 2.5 Causal Structure and Penrose Diagrams 73 2.6 Anti-de Sitter Spacetime and Holography 78 2.6.1 Stereographic Projection and Hyperbolic Geometry 79 2.6.2 The Geometry of Anti-de Sitter Spacetime 82 2.6.3 Holography: The AdS/CFT Correspondence 86 References 90 3 The Positive Mass Theorem, Stability, and Phase Transitions 93 3.1 Defining Mass in General Relativity 93 3.2 Positive Mass and Stability 102 3.3 The Euclidean Action 105 3.4 Phase Transitions Between Spacetimes 109 References 115 4 Hiscock and Weems: Modeling the Hawking Evaporation of Asymptotically Flat Charged Black Holes 118 4.1 Black Hole Evolution and Cosmic Censorship 118 4.2 Reissner--Nordström Black Holes Revisited 120 4.3 The Hiscock and Weems Model 123 References 135 5 Why Hawking Radiation Cannot Be Decoded 137 5.1 Information Decoding Versus the Lifetimes of Charged Black Holes 137 5.2 Evaporating Charged AdS Black Holes 146 5.3 Thermodynamics of Charged Evaporating Flat Black Holes 153 5.4 Fatal Attraction Toward Extremality 159 5.5 Charge Loss (or the Lack Thereof) for AdS Black Holes 166 5.6 Conclusion: Hawking Radiation Cannot be Decoded 174 References 175 6 Slaying Monsters: Do Hyper-Entropic Objects Exist in Quantum Gravity? 179 6.1 The Large Volume of Black Holes 179 6.2 A Monster Is Born 183 6.3 Monsters in String Theory 188 6.4 Collapsing Versus Destabilizing a Monster 197 6.5 The Fate of Monsters 198 References 201 Appendix AEpilogue 203 Appendix BThe Path Integral and Thermodynamics 206 Appendix CQuantum Information 215 Appendix DBrane-Pair Production via Seiberg-WittenInstability 229 Front Matter....Pages i-xxii A Century of Black Hole Physics: From Classical Geometry to Hawking Radiation and the Firewall Controversy....Pages 1-35 General Relativity: Subtle Is the Lord....Pages 37-73 The Positive Mass Theorem, Stability, and Phase Transitions....Pages 75-99 Hiscock and Weems: Modeling the Hawking Evaporation of Asymptotically Flat Charged Black Holes....Pages 101-119 Why Hawking Radiation Cannot Be Decoded....Pages 121-162 Slaying Monsters: Do Hyper-Entropic Objects Exist in Quantum Gravity? ....Pages 163-186 Back Matter....Pages 187-222