This textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning.
The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.
Author(s): Daniel Grumiller, Mohammad Mehdi Sheikh-Jabbari
Series: Graduate Texts in Physics
Publisher: Springer
Year: 2022
Language: English
Pages: 430
City: Cham
Foreword
Preface
How to Read and Use This Book
Acknowledgements
Contents
Acronyms
Notations and Conventions
List of Figures
1 Introduction
1.1 Essentials of General Relativity
1.1.1 Equivalence Principle and Geodesics
1.1.2 Einstein Gravity
1.2 Brief Review of Black Hole History
1.2.1 First Five Decades: Finding Solutions and Classic Analyses
1.2.2 Black Holes Through Observations
1.2.3 Black Holes as Thermodynamical Systems
1.3 Gravitational Collapse in Stars
1.3.1 Core Collapse Supernova and Black Hole Formation
1.3.2 Estimating the Chandrasekhar Mass
1.4 Different Schools of Thought on Black Holes
1.4.1 GR School
1.4.2 HEP School
1.4.3 Quantum Information School
2 Black Hole Solutions and Basic Properties
2.1 Schwarzschild Metric, Basic Facts, and Analyses
2.1.1 Symmetries and Killing Vectors
2.1.2 Flamm Diagram
2.1.3 Singularities, Asymptotic, and Near Horizon Behavior
2.1.4 ADM Mass and Angular Momentum
2.1.5 Infinite Redshift Surface
2.2 Particle Probes and Geodesics
2.2.1 Null Geodesics
2.2.2 Timelike Geodesics and Particle Orbits
2.2.3 Eddington–Finkelstein Coordinates
2.3 Maximal Extensions and Causal Diagrams
2.3.1 Geodesic Completeness and Maximal Analytic Extension
2.3.2 Kruskal Coordinates for Schwarzschild Geometry
2.3.3 Structure of Lightcones and Preliminary Notion of Horizon
2.3.4 Carter–Penrose Causal Diagrams
2.3.5 Realistic Black Holes and Wormholes
2.4 Einstein–Maxwell Theory and Reissner–Nordström Black Holes
2.5 Kerr Solution and Its Basic Analysis
2.5.1 Basic Properties of Kerr Black Hole
2.5.2 Geodesics of Kerr Geometry
2.6 Black Holes in (A)dS Backgrounds
2.6.1 Schwarzschild-dS Black Holes
2.6.2 Schwarzschild-AdS and Topological Black Holes
2.7 Plebanski–Demianski Black Holes
2.8 Vaidya Metric as Example for Non-stationary Black Holes
3 Formal Definitions and Classic Theorems
3.1 Mathematical Definitions of Black Holes and Horizons
3.1.1 Killing Horizon and Surface Gravity
3.1.2 Event Horizon and Mathematical Black Hole Definition
3.1.3 Apparent Horizons and Trapped Surfaces
3.1.4 Cauchy Horizons and Predictability
3.1.5 Other Horizon Definitions
3.2 Classic Conjectures and Theorems
3.2.1 Raychaudhuri Equation
3.2.2 Classical Energy Conditions
3.2.3 Singularity Theorems
3.2.4 Asymptotic Flatness
3.2.5 Horizon Theorems
3.2.6 Uniqueness Theorems
3.2.7 Cosmic Censorship Conjecture
3.3 Optical Focusing Equation and Area Theorem (2nd Law)
4 Probing Black Holes, Their Formation and Stability
4.1 General Remarks on Black Hole Observations
4.2 Black Hole Photon-Sphere, Shadows, and Images
4.3 Penrose Process, Super-Radiance, and Black Hole Mining
4.4 Gravitational Waves and Black Hole Mergers
4.5 Accretion Disk Physics
4.6 Black Hole Formation in Shock-Wave Collisions
4.7 Black Hole Perturbations and Linear Stability
4.7.1 Quasi-normal Modes
4.7.2 Late-Time Tails and Linearized Stability
4.7.3 Perturbative Aspects of Black Hole Binaries
4.8 Gravitational Collapse and Non-linear Stability
4.8.1 Critical Collapse and Choptuik Exponent
4.8.2 On Non-linear Stability of Black Hole Solutions
5 Black Hole Charges and Thermodynamics
5.1 Introduction to Systematic Methods for Charge Computation
5.2 Komar Charges
5.3 Solution Phase Space Method
5.3.1 Solution Space Is a Phase Space
5.3.2 Exact Symmetries and the Associated Charges
5.4 Entropy as a Conserved Charge
5.4.1 Entropy as a Noether Charge
5.4.2 Entropy and Solution Phase Space Method
5.4.3 Entropy in Cases Involving Gauge Fields
5.5 Four Laws of Black Hole Thermodynamics
5.5.1 Zeroth Law
5.5.2 First Law and Its Derivation
5.5.3 Second Law and Its Generalizations
5.5.4 Third Law and Extremal Black Holes
6 Semiclassical Aspects of Black Holes
6.1 Variational Principle
6.1.1 Gibbons–Hawking–York Boundary Term
6.1.2 Brown–York Stress Tensor
6.2 Quantization on Black Hole Backgrounds
6.3 Unruh Effect
6.3.1 Unruh Vacuum State
6.3.2 Unruh Temperature, Bogoliubov Transformations
6.3.3 Unruh Temperature, Euclidean Field Theory Analysis
6.3.4 Discussion
6.4 Hawking Effect
6.4.1 Heuristics of Hawking Effect from Vacuum Fluctuations
6.4.2 Hawking Temperature from Euclidean Continuation
6.4.3 Hawking Radiation from Ray-Tracing
6.4.4 Hawking Radiation from Anomalies
6.4.5 Greybody Factors
6.4.6 Discussion
6.5 Black Hole Entropy and Alternative Derivations
6.5.1 Euclidean Effective Action and Gibbons–Hawking Derivation
6.5.2 Entropy Bounds
6.6 Parikh–Wilczek Tunneling
6.6.1 Painlevé Coordinates
6.6.2 Painlevé–Parikh–Wilczek Vacuum
6.6.3 Discussion of Parikh–Wilczek Tunneling
6.7 Black Hole Evaporation
6.8 Membrane Paradigm
6.8.1 Membrane Action and Dynamics, Classical Analysis
6.8.2 Membrane Action, Semiclassical Analysis
6.9 Information Puzzle and Apparent Loss of Unitarity
7 Gravity and Black Holes in Diverse Dimensions
7.1 Why Gravity in Lower Dimensions?
7.2 Gravity in Three Dimensions
7.2.1 BTZ Black Holes and Bañados Geometries
7.2.2 Chern–Simons Formulation
7.2.3 Canonical Boundary Charges
7.2.4 Alternative Boundary Conditions to Brown–Henneaux
7.2.5 Beyond AdS3 Einstein Gravity
7.3 Gravity in Two Dimensions
7.3.1 Jackiw–Teitelboim Model
7.3.2 Generic Dilaton Gravity
7.3.3 Gauge Theoretic Formulation
7.3.4 All Classical Solutions, Locally and Globally
7.4 Why Gravity in Higher Dimensions?
7.5 Higher-Dimensional Black Hole/Ring/Brane Solutions
7.5.1 Tangherlini Solution
7.5.2 Myers–Perry Black Holes
7.5.3 Five-Dimensional Black Ring Solution
7.5.4 Asymptotic AdS Vacuum Black Hole Solutions
7.5.5 Black Branes
7.6 Black Holes in Large Number of Dimensions
8 Aspects of Holography
8.1 Basics of Holography
8.1.1 AdS/CFT, the Precise Statement
8.1.2 Gravity in Anti-De Sitter Space
8.1.3 Holographic Renormalization
8.1.4 Holographic Correlation Functions
8.2 Holography and Quantum Information
8.3 AdS Black Holes and Holography
8.3.1 Black Holes as Thermal States
8.3.2 Hawking–Page Phase Transition
8.3.3 Eternal Black Holes
8.4 Asymptotic Symmetries
8.5 Soft Hair and Near Horizon Symmetries
8.6 Extremal Black Holes and Attractor Mechanism
8.6.1 Symmetry Enhancement
8.6.2 Attractor Mechanism
8.7 Kerr/CFT and Related Topics
8.8 Summary and Outlook
Further Reading
9 Quantum Aspects of Black Holes
9.1 Black Holes and Quantum Gravity
9.2 Black Hole Complementarity, Firewalls, Page Curve and Islands
9.3 Black Holes in String Theory
9.3.1 D1-D5-P System
9.3.2 Breckenridge–Myers–Peet–Vafa Solution
9.4 Microstate Counting
9.4.1 Microstate Counting for BTZ Black Holes
9.4.2 Microstate Counting for D1-D5-P and Breckenridge–Myers–Peet–Vafa Black Hole
9.5 Microstate Identification, Fuzzball and Fluffball Proposals
9.5.1 Fuzzball Proposal, Microstate Geometries
9.5.2 Soft Hair Proposal and Its Fluffball Realization
9.6 Information Puzzle and AdS/CFT
10 Outlook
10.1 Summary of the Book
10.2 Open Conceptual Issues
10.3 Observational Prospects
A Variational Identities
B p-Forms
C Cartan Formulation
Exercises
D Teukolsky Equation
D.1 Newman–Penrose Formalism Applied to Kerr
D.2 Teukolsky Master Equation as Heun Equation
D.3 Remarks on the Teukolsky Equation for Vanishing Spin
Exercises
E Basics of QFT in Curved Spacetime
Exercises
F ADM 3+1 Decomposition
Exercises
G Covariant Phase Space Formalism
Exercises
H More on Membrane Paradigm
Exercises
I String Theory Low Energy Effective Actions
Exercises
J Hints to Some Selected Exercises
Exercises of Chapter 1摥映數爠eflinkchap:intro11
Exercises of Chapter 2摥映數爠eflinkchap:basics22
Exercises of Chapter 3摥映數爠eflinkchap:advancedspsconcepts33
Exercises of Chapter 4摥映數爠eflinkchap:classicalspsaspects44
Exercises of Chapter 5摥映數爠eflinkchap:chargesspsthermo55
Exercises of Chapter 6摥映數爠eflinkchap:seminclassical66
Exercises of Chapter 7摥映數爠eflinkchap:expert77
Exercises of Chapter chap:holography
Exercises of Chapter chap:quantum
Exercises of Appendix A
Exercises of Appendix B
Exercises of Appendix C
Exercises of Appendix D
Exercises of Appendix E
Exercises of Appendix F
Exercises of Appendix G
Exercises of Appendix H
Exercises of Appendix I
References
