Quantum Aspects of Black Holes (Fundamental Theories of Physics Book 178)

Beginning With An Overview Of The Theory Of Black Holes By The Editor, This Book Presents A Collection Of Ten Chapters By Leading Physicists Dealing With The Variety Of Quantum Mechanical And Quantum Gravitational Effects Pertinent To black Holes. The Contributions Address Topics Such As Hawking Radiation, The Thermodynamics Of Black Holes, The Information Paradox And Firewalls, Monsters, Primordial Black Holes, Self-gravitating Bose-einstein Condensates, The Formation Of Small Black Holes In High Energetic Collisions Of Particles, Minimal Length Effects In Black Holes And Small Black Holes At The Large Hadron Collider. Viewed As A Whole The Collection Provides Stimulating Reading For Researchers And Graduate Students Seeking A Summary Of The Quantum Features Of Black Holes. Fundamental Physics With Black Holes (xavier Calmet) -- Black Holes And Thermodynamics - The First Half Century (daniel Grumiller, Robert Mcnees And Jakob Salzer) -- The Firewall Phenomenon (r. B. Mann) -- Monsters, Black Holes And Entropy (stephen D. H. Hsu) -- Primordial Black Holes: Sirens Of The Early Universe (anne M. Green) -- Self-gravitating Bose-einstein Condensates (pierre-henri Chavanis) -- Quantum Amplitudes In Black-hole Evaporation With Local Supersymmetry (p.d.d'eath And A.n.st.j.farley) -- Hawking Radiation From Higher-dimensional Black Holes (panagiota Kanti And Elizabeth Winstanley) -- Black Holes At The Large Hadron Collider (greg Landsberg) -- minimum Length Effects In Black Hole Physics (roberto Casadio, Octavian Micu, Piero Nicolini). Edited By Xavier Calmet. Preface 6 Contents 8 1 Fundamental Physics with Black Holes 13 1.1 Introduction 13 1.2 Quantum Black Holes 16 1.3 Low Scale Quantum Gravity and Black Holes at Colliders 17 1.4 An Effective Theory for Quantum Gravity 23 1.5 Quantum Black Holes in Loops 25 1.6 Quantum Black Holes and the Unification of General Relativity and Quantum Mechanics 28 1.7 Quantum Black Holes, Causality and Locality 32 1.8 Conclusions 35 References 36 2 Black Holes and Thermodynamics: The First Half Century 39 2.1 Introduction and Prehistory 39 2.2 1963--1973 41 2.3 1973--1983 45 2.4 1983--1993 51 2.5 1993--2003 57 2.6 2003--2013 62 2.7 Conclusions and Future 68 References 69 3 The Firewall Phenomenon 83 3.1 Introduction 83 3.2 Black Holes 84 3.2.1 Gravitational Collapse 87 3.2.2 Anti de Sitter Black Holes 89 3.3 Black Hole Thermodynamics 90 3.4 Black Hole Radiation 92 3.4.1 Quantum Field Theory in Curved Spacetime 92 3.4.2 Pair Creation 95 3.5 The Information Paradox 100 3.5.1 Implications of the Information Paradox 106 3.5.2 Complementarity 107 3.6 Firewalls 110 3.6.1 The Firewall Argument 110 3.6.2 Responses to the Firewall Argument 112 3.7 Summary 119 References 120 4 Monsters, Black Holes and Entropy 126 4.1 Introduction 126 4.2 What is Entropy? 127 4.3 Constructing Monsters 128 4.3.1 Monsters 129 4.3.2 Kruskal--FRW Gluing 131 4.4 Evolution and Singularities 134 4.5 Quantum Foundations of Statistical Mechanics 135 4.6 Statistical Mechanics of Gravity? 137 4.7 Conclusions 138 References 139 5 Primordial Black Holes: Sirens of the Early Universe 140 5.1 Introduction 140 5.2 PBH Formation Mechanisms 141 5.2.1 Large Density Fluctuations 141 5.2.2 Cosmic String Loops 143 5.2.3 Bubble Collisions 143 5.3 PBH Abundance Constraints 144 5.3.1 Evaporation 144 5.3.2 Lensing 146 5.3.3 Dynamical Effects 147 5.3.4 Other Astrophysical Objects and Processes 148 5.4 Constraints on the Primordial Power Spectrum and Inflation 149 5.4.1 Translating Limits on the PBH Abundance into Constraints on the Primordial Power Spectrum 150 5.4.2 Constraints on Inflation Models 152 5.5 PBHs as Dark Matter 153 5.6 Summary 154 References 155 6 Self-gravitating Bose-Einstein Condensates 161 6.1 Introduction 162 6.2 Self-gravitating Bose-Einstein Condensates 165 6.2.1 The Gross-Pitaevskii-Poisson System 165 6.2.2 Madelung Transformation 166 6.2.3 Time-Independent GP Equation 168 6.2.4 Hydrostatic Equilibrium 168 6.2.5 The Non-interacting Case 169 6.2.6 The Thomas-Fermi Approximation 170 6.2.7 Validity of the Thomas-Fermi Approximation 171 6.2.8 The Total Energy 172 6.2.9 The Virial Theorem 173 6.3 The Gaussian Ansatz 173 6.3.1 The Total Energy 174 6.3.2 The Mass-Radius Relation 174 6.3.3 The Virial Theorem 179 6.3.4 The Pulsation Equation 179 6.4 Application of Newtonian Self-gravitating BECs to Dark Matter Halos 180 6.4.1 The Non-interacting Case 180 6.4.2 The Thomas-Fermi Approximation 180 6.4.3 Validity of the Thomas-Fermi Approximation 182 6.4.4 The Case of Attractive Self-interactions 182 6.5 Application of General Relativistic BECs to Neutron Stars, Dark Matter Stars, and Black Holes 183 6.5.1 Non-interacting Boson Stars 184 6.5.2 The Thomas-Fermi Approximation for Boson Stars 185 6.5.3 Validity of the Thomas-Fermi Approximation 187 6.5.4 An Interpolation Formula Between the Non-interacting Case and the TF Approximation 187 6.5.5 Application to Supermassive Black Holes 188 6.5.6 Application to Neutron Stars and Dark Matter Stars 189 6.5.7 Are Microscopic Quantum Black Holes Bose-Einstein Condensates of Gravitons? 190 6.6 Conclusion 192 6.7 Self-interaction Constant 195 6.8 Conservation of Energy 195 6.9 Virial Theorem 196 6.10 Stress Tensor 197 6.11 Lagrangian and Hamiltonian 199 References 201 7 Quantum Amplitudes in Black--Hole Evaporation with Local Supersymmetry 205 7.1 Introduction 206 7.2 `Semi--Classical' Amplitudes 207 7.2.1 Locally--Supersymmetric Quantum Mechanics 207 7.2.2 N = 1 Supergravity: Dirac Approach 211 7.2.3 The Quantum Constraints 214 7.2.4 `Semi--Classical' Amplitude in N = 1 Supergravity 217 7.3 Quantum Amplitudes in Black--Hole Evaporation 221 7.3.1 Introduction 221 7.3.2 The Quantum Amplitude for Bosonic Boundary Data 222 7.3.3 Classical Action and Amplitude for Weak Perturbations 226 7.3.4 Comments 235 References 236 8 Hawking Radiation from Higher-Dimensional Black Holes 239 8.1 Introduction 239 8.2 Hawking Radiation 241 8.2.1 Hawking Radiation from a Black Hole Formed by Gravitational Collapse 241 8.2.2 The Unruh State 244 8.3 Brane World Black Holes 247 8.3.1 Black Holes in ADD Brane-Worlds 247 8.3.2 Black Holes in RS Brane-Worlds 249 8.4 Hawking Radiation from Black Holes in the ADD Model 250 8.4.1 Formalism for Field Perturbations 250 8.4.2 Grey-Body Factors and Fluxes 254 8.4.3 Emission of Massless Fields on the Brane 256 8.4.4 Emission of Massless Fields in the Bulk 262 8.4.5 Energy Balance Between the Brane and the Bulk 266 8.4.6 Additional Effects in Hawking Radiation 267 8.5 Hawking Radiation from Black Holes in the RS Model 268 8.6 Conclusions 271 References 272 9 Black Holes at the Large Hadron Collider 276 9.1 Introduction 276 9.2 Low-Scale Gravity Models 277 9.2.1 Probing the ADD Model at the LHC 278 9.2.2 Probing the RS Model at the LHC 280 9.3 Black Hole Phenomenology 281 9.3.1 Black Hole Production in Particle Collisions 283 9.3.2 Black Hole Evaporation 284 9.3.3 Accounting for the Black Hole Angular Momentum and Grey-Body Factors 287 9.3.4 Simulation of Black Hole Production and Decay 289 9.3.5 Randall--Sundrum Black Holes 290 9.3.6 Limits on Semiclassical Black Holes 292 9.3.7 Limits on Quantum Black Holes and String Balls 296 9.4 Conclusions 299 References 299 10 Minimum Length Effects in Black Hole Physics 302 10.1 Gravity and Minimum Length 302 10.2 Minimum Black Hole Mass 304 10.2.1 GUP, Horizon Wave-Function and Particle Collisions 305 10.2.2 Regular Black Holes 311 10.3 Extra Dimensions 318 10.3.1 Black Holes in Extra Dimensions 318 10.3.2 Minimum Mass and Remnant Phenomenology 322 10.4 Concluding Remarks 327 References 327 Front Matter....Pages i-xi Fundamental Physics with Black Holes....Pages 1-26 Black Holes and Thermodynamics: The First Half Century....Pages 27-70 The Firewall Phenomenon....Pages 71-113 Monsters, Black Holes and Entropy....Pages 115-128 Primordial Black Holes: Sirens of the Early Universe....Pages 129-149 Self-gravitating Bose-Einstein Condensates....Pages 151-194 Quantum Amplitudes in Black–Hole Evaporation with Local Supersymmetry....Pages 195-228 Hawking Radiation from Higher-Dimensional Black Holes....Pages 229-265 Black Holes at the Large Hadron Collider....Pages 267-292 Minimum Length Effects in Black Hole Physics....Pages 293-322