Hawking Radiation: From Astrophysical Black Holes To Analogous Systems In Lab

by Francesco D Belgiorno, Sergio L Cacciatori, Daniele Faccio

Overview

'The book can be a good introduction to research in the area of black hole physics. Also, it can serve as a source book for the established researcher in the field. The book contains an extensive bibliography the contents of which are amply cited throughout the text. The book well documents the historical development of the theory of Hawking radiation and related topics. The book is a worthwhile addition to the physics literature on a topic of considerable interest.'
zbMATHThe aim of this book is to provide the reader with a guide to Hawking radiation through a dual approach to the problem. After an introductory chapter containing some basic knowledge about black holes and quantum field theory in curved spacetime, the first part of the book consists in a survey of methods for deriving and studying Hawking radiation from astrophysical black holes, from the original calculation by S W Hawking to the most recent contributions involving tunneling and gravitational anomalies. In the second part, we introduce analogue gravity, and we focus our attention to dielectric black hole systems, to which the studies of the present authors are devoted. The mutual interchange of knowledge between the aforementioned parts is addressed to render a more comprehensive picture of this very fascinating quantum phenomenon associated with black holes.

Product Details

ISBN-13:	9789814508537
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	08/23/2018
Pages:	340
Product dimensions:	6.00(w) x 9.00(h) x 0.81(d)

Table of Contents

Introduction xiii

First Part 1

1 A short scrapbook on classical black holes 3

1.1 Mathematical black holes 3

1.2 Schwarzschild and Kerr black holes 6

1.2.1 The Schwarzschild black hole 6

1.2.2 The Kerr black hole 10

1.3 Bifurcate Killing horizons 15

1.4 Quantum fields and particles 19

1.4.1 The Boulware state 20

1.4.2 The Hartle-Hawking state 21

1.4.3 The Unruh state 22

1.5 BMS group for asymptotically flat spacetimes 23

1.6 Further readings 26

2 The seminal paper 27

2.1 Particle creation by black holes: The computation 31

2.2 Particle creation by black holes: Dependence on the details 45

2.2.1 Nonsymmetrical collapse 45

2.2.2 The spin of the fields 47

2.2.3 Massive fields 48

2.2.4 Angular momentum 49

2.2.5 Electric charge 50

2.2.6 Back reaction 51

2.3 A Very short list of further readings 55

3 Thermality of Hawking radiation: From Hartle-Hawking to Israel and Unruh 57

3.1 Hartle-Hawking approach to black hole radiance 58

3.2 Gibbons-Perry analysis for thermality 64

3.3 Thermofield dynamics and Hartle-Hawking-Israel state 66

3.3.1 Thermofield Dynamics 66

3.3.2 Israel contribution 68

3.4 Unruh's cornerstone 71

4 The tunneling approach 73

4.1 Damour-Ruffini 74

4.2 Hamilton-Jacobi tunneling method 76

4.2.1 Canonical invariance 78

4.2.2 The null geodesic method 78

4.2.3 The analyticity argument 81

4.2.4 A trick à la Nikishov 83

4.2.5 The 4D case: Role of the transverse coordinates 86

4.3 Parikh-Wilczek approach 87

5 The anomaly route to Hawking radiation 89

5.1 Christensen-Fulling way (1977) 89

5.2 Robinson-Wilczek (2005) and Iso-Umetsu-Wilczek (2006) 93

6 The Euclidean section and Hawking temperature 101

6.1 Local diffeomorphism and extendability 102

6.2 Conical singularity and black hole horizon 104

6.2.1 The 2D case 104

6.2.2 The 4D case 105

6.3 The Hawking temperature from the extendability of the metric at r = r₊ 106

6.4 Example: Schwarzschild black hole 108

6.5 The failure of the argument for extremal black holes 108

7 Rigorous aspects of Hawking radiation 111

7.1 Local definiteness principle and local stability 112

7.1.1 The local definiteness 113

7.2 Hawking temperature from local definiteness and stability 115

7.3 Existence of Hartle-Hawking state 120

7.3.1 Almost free double quantum dynamical systems 120

7.3.2 The Minkowski vacuum 124

7.3.3 The Hartle-Hawking state 127

7.3.4 The Boulware one particle structure 129

7.4 Hawking temperature for a spacetime with bifurcated Killing horizon 131

7.4.1 Modular inclusion and Hawking temperature 131

7.5 Further readings for black holes of the Kerr-Newman family 133

Second Part 135

8 The roots of analogue gravity 137

8.1 Experimental black hole evaporation in water 138

8.2 Analogue systems and dispersion: The Gospel according to Unruh 141

8.3 A sample model for dispersive fluids: Essentials 144

8.4 Analogue gravity in BEC 147

8.5 Further readings concerning analogue gravity in presence of dispersion 150

9 Hawking radiation in a non-dispersive nonlinear Kerr dielectric 153

9.1 Classical analysis of the effective spacetime geometry 154

9.1.1 Wave rays geometry in the RIP frame 157

9.1.2 Horizons in effective geometries 159

9.1.3 Null geodesies in dispersionless and in dispersive dielectrics 163

9.1.4 Trapping in dispersive regime 168

9.2 Hawking radiation in a static dielectric black hole 170

9.2.1 The "standard" Hawking prediction 175

9.2.2 The electrodynamics point of view 177

9.3 Effects of optical dispersion: Preliminary heuristics 185

9.3.1 Horizons in dispersive media 188

10 Hawking radiation in a dispersive Kerr dielectric 195

10.1 The relativistic Hopfield model 196

10.1.1 The covariant generalization of the Hopfield model 197

10.1.2 Quantum covariant Hopfield model 199

10.2 Uniformly moving RIP 214

10.3 Hawking radiation in the perturbative formulation 216

10.3.1 The φφ-model 217

10.3.2 Separation of variables 220

10.3.3 Quantization of the fields 221

10.4 An interlude: Semi-analytical and numerical calculations from Maxwell equations in the lab 228

10.4.1 Born approximation 229

10.4.2 Thermality for a Gaussian perturbation 231

10.4.3 A sample of numerical results 233

10.5 Calculation of thermality in the φφ model 234

10.5.1 Determination of the microscopic parameters in terms of the physical ones 236

10.5.2 Near horizon approximation: Solutions of equation (10.232) 237

10.5.3 Steepest descent approximation 238

10.5.4 Convergence regions 241

10.5.5 Decreasing mode inside the black hole x < 0 241

10.5.6 Possible diagrams in the external region x > 0 241

10.5.7 Special configurations and thermality of pair-creation 242

10.5.8 Branch cuts along steepest descent paths 245

10.5.9 Vertical branch cuts 246

10.5.10 Near horizon: A different saddle point approximation 249

10.5.11 WKB solutions 252

10.5.12 A dimensionless parameter for the saddle point approximation 255

10.5.13 A further repealing and insights for thermality 257

10.5.14 Coalescence of branch points as ω → 0 259

10.5.15 Horizons and dispersion 261

10.6 Recapitulation 263

10.7 Further readings 264

10.8 Hawking radiation in a dispersive nonlinear dielectric 265

11 Hawking radiation in the lab 267

11.1 The Como experiment 267

11.2 The Vancouver experiment 276

11.3 The Technion experiment 278

Appendix A Algebraic methods in QFT 281

A.1 Araki-Haag-Kastler algebraic formulation of QFT 281

A.2 Haag-Hugenholz-Winnik formulation of quantum statistical systems 286

A.2.1 Structure of the statistical system 286

A.2.2 The Gibbs states 289

A.2.3 KMS condition and the infinite volume limit 290

A.2.4 The thermal representations 292

A.3 The Tomita-Takesaki theorem 294

A.3.1 Polar decomposition 294

A.3.2 Some simple facets about Von Neumann algebras 295

A 3.3 The Tomita-Takesaki theorem and the KMS condition 297

Bibliography 299

Index 321