| Preface | |
| Notation and Conventions | |
| Fundamentals | |
| Introduction | |
| Introduction | |
| Space and Time in Prerelativity Physics and in Special Relativity | |
| The Spacetime Metric | |
| General Relativity | |
| Manifolds and Tensor Fields | |
| Manifolds | |
| Vectors | |
| Tensors; the Metric Tensor | |
| The Abstract Index Notation | |
| Curvature | |
| Derivative Operators and Parallel Transport | |
| Curvature | |
| Geodesics | |
| Methods for Computing Curvature | |
| Einstein's Equation | |
| The Geometry of Space in Prerelativity Physics; General and Special Covariance | |
| Special Relativity | |
| General Relativity | |
| Linearized Gravity: The Newtonian Limit and Gravitational Radiation | |
| Homogeneous, Isotropic Cosmology | |
| Homogeneity and Isotrophy | |
| Dynamics of a Homogeneous, Isotropic Universe | |
| The Cosmological Redshift; Horizons | |
| The Evolution of Our Universe | |
| The Schwartzschild Solution | |
| Derivation of the Schwartzschild Solution | |
| Interior Solutions | |
| Geodesics of Schwartzschild: Gravitation Redshift, Perihelion Precession, Bending of Light, and Time Delay | |
| The Kruskal Extension | |
| Advanced Topics | |
| Methods for Solving Einstein's Equation | |
| Stationary, Axisymmetric Solutions | |
| Spatially Homogeneous Cosmologies | |
| Algebraically Special Solutions | |
| Methods for Generating Solutions | |
| Perturbations | |
| Casual Structure | |
| Futures and Pasts: Basic Definitions and Results | |
| Causality Conditions | |
| Domains of Dependence; Global Hyperbolicity | |
| Singularities | |
| What is a Singularity? | |
| Timelike and Null Geodesic Congruences | |
| Conjugate Points | |
| Existence of Maximum Length Curves | |
| Singularity Theorems | |
| The Initial Value Formulation | |
| Initial Value Formulation for Particles and Fields | |
| Initial Value Formulation of General Relativity | |
| Asymptotic Flatness | |
| Conformal Infinity | |
| Energy | |
| Black Holes | |
| Black Holes and the Cosmic Censor Conjecture | |
| General Properties of Black Holes | |
| The Charged Kerr Black Holes | |
| Energy Extraction from Black Holes | |
| Black Holes and Thermodynamics | |
| Spinors | |
| Spinors in Minkowski Spacetime | |
| Spinors in Curved Spacetime | |
| Quantum Effects in Strong Gravitational Fields | |
| Quantum Gravity | |
| Quantum Fields in Curved Spacetime | |
| Particle Creation near Black Holes | |
| Black Hold Thermodynamics | |
| Appendices | |
| Topological Spaces | |
| Differential Forms, Integration, and Frobenius's Theorem | |
| Differential Forms | |
| Integration | |
| Frobenius's Theorem | |
| Maps of Manifolds, Lie Derivatives, and Killing Fields | |
| Maps of Manifolds | |
| Lie Derivatives | |
| Killing Vector Fields | |
| Conformal Transformations | |
| Lagrangian and Hamiltonian Formulations of Einstein's Equation | |
| Lagrangian Formulation | |
| Hamiltonian Formulation | |
| Units and Dimensions | |
| References | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
