Intro
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