Preface -- Contents -- Chapter 1 Introduction -- Chapter 2 Classical Black Holes -- 2.1 Modeling the Gravitational Collapse -- 2.1.1 The Oppenheimer-Snyder model -- 2.1.2 Non-spherical collapse -- 2.2 The Schwarzschild Black Hole -- 2.2.1 Eddington-Finkelstein coordinates -- 2.2.2 Kruskal coordinates -- 2.3 Causal Structure and Penrose Diagrams -- 2.3.1 Minkowski space -- 2.3.2 Schwarzschild spacetime -- 2.4 Kruskal and Locally Inertial Coordinates at the Horizons -- 2.4.1 Redshift factors and surface gravity -- 2.5 Charged Black Holes -- 2.6 The Extremal Reissner-Nordström Black Hole -- 2.7 Rotating Black Holes -- 2.7.1 Energy extraction from rotating black holes: the Penrose process -- 2.8 Trapped Surfaces, Apparent and Event Horizons -- 2.8.1 The area law theorem -- 2.9 The Laws of Black Hole Mechanics -- 2.10 Stringy Black Holes -- Chapter 3 The Hawking Effect -- 3.1 Canonical Quantization in Minkowski Space -- 3.2 Quantization in Curved Spacetimes -- 3.2.1 Bogolubov transformations and particle production -- 3.3 Hawking Radiation in Vaidya Spacetime -- 3.3.1 Ingoing and outgoing modes -- 3.3.2 Wave packets -- 3.3.3 Wick rotation -- 3.3.4 Planck spectrum -- 3.3.5 Uncorrelated thermal radiation -- 3.3.6 Where are the correlations? -- 3.3.7 Thermal density matrix -- 3.4 Including the Backscattering -- 3.4.1 Waves in the Schwarzschild geometry -- 3.4.2 Late-time basis to accommodate backscattering -- 3.4.3 Thermal radiation and grey-body factors -- 3.4.4 Estimations for the luminosity -- 3.5 Importance of the Backreaction -- 3.6 Late-Time Independence on the Details of the Collapse -- 3.6.1 The example of two shock waves -- 3.6.2 Geometric optics approximation -- 3.6.3 General collapse -- 3.6.4 Adding angular momentum and charge -- 3.7 Black Hole Thermodynamics -- 3.8 Physical Implications of Black Hole Radiance and the Information Loss Paradox.

3.8.1 Black hole evaporation -- 3.8.2 Breakdown of quantum predictability -- 3.8.3 Alternatives to restore quantum predictability -- Chapter 4 Near-Horizon Approximation and Conformal Symmetry -- 4.1 Rindler Space -- 4.2 Conformal Symmetry, Stress Tensor and Particle Number -- 4.2.1 The normal ordered stress "tensor" operator -- 4.2.2 The SO(d,2) conformal group and Möbius transformations -- 4.2.3 The particle number operator -- 4.3 Radiation in Rindler Space: Hawking and Unruh Effects -- 4.3.1 The Hawking effect -- 4.3.2 Radiation through the horizon -- 4.3.3 The Unruh effect -- 4.3.4 Three different vacuum states -- 4.4 Anti-de Sitter Space as a Near-Horizon Geometry -- 4.4.1 Extremal black holes -- 4.4.2 Near-extremal black holes -- 4.5 Radiation in Anti-de Sitter Space: the Hawking Effect -- 4.5.1 Three vacuum states -- 4.6 The Moving-Mirror Analogy for the Hawking Effect -- 4.6.1 Exponential trajectory: thermal radiation -- 4.6.2 Radiationless trajectories -- 4.6.3 Asymptotically inertial trajectories and unitarity -- Chapter 5 Stress Tensor, Anomalies and Effective Actions -- 5.1 Relating the Virasoro and Trace Anomalies via Locally Inertial Coordinates -- 5.2 The Polyakov Effective Action -- 5.2.1 The role of the Weyl-invariant effective action -- 5.3 Choice of the Quantum State -- 5.3.1 Boulware state -- 5.3.2 Hartle-Hawking state -- 5.3.3 The "in" and Unruh vacuum states: the Hawking flux -- 5.4 Including the Backscattering in the Stress Tensor: the s-wave -- 5.4.1 Two-dimensional symmetries -- 5.4.2 The normal ordered stress tensor -- 5.4.3 The covariant quantum stress tensor -- 5.4.4 Effective action -- 5.4.5 Quantum states and Hawking flux -- 5.5 Beyond the s-wave Approximation -- 5.6 The Problem of Backreaction -- 5.6.1 Backreaction equations from spherical reduction -- 5.6.2 The problem of determining the state-dependent functions.

5.6.3 Returning to the near-horizon approximation -- Chapter 6 Models for Evaporating Black Holes -- 6.1 The Near Horizon Approximation -- 6.1.1 Schwarzschild -- 6.1.2 Near-extremal Reissner-Nordström black holes: the JT model -- 6.1.3 Near-extremal dilaton black holes -- 6.2 The CGHS Model -- 6.2.1 The CGHS black hole -- 6.2.2 Including matter fields -- 6.2.3 Bogolubov coefficients and Hawking radiation -- 6.2.4 Quantum states for the CGHS black hole -- 6.3 The Problem of Backreaction in the CGHS Model -- 6.3.1 State-dependent functions for evaporating black holes -- 6.3.2 The RST model -- 6.3.3 Black hole evaporation in the RST model -- 6.4 The Semiclassical JT Model -- 6.4.1 Extremal solution -- 6.4.2 Semiclassical static solutions -- 6.4.3 General solutions -- 6.4.4 Black hole evaporation in the JT model -- 6.4.5 Beyond the near-horizon approximation and Hawking radiation -- 6.4.6 Information loss in the JT model -- 6.4.7 Unitarity in the semiclassical approximation? -- Bibliography -- Index.