Preface |
Notation and Conventions |
Fundamentals / Part I: |
Introduction / 1: |
Space and Time in Prerelativity Physics and in Special Relativity / 1.1: |
The Spacetime Metric / 1.3: |
General Relativity / 1.4: |
Manifolds and Tensor Fields / 2: |
Manifolds / 2.1: |
Vectors / 2.2: |
Tensors; the Metric Tensor / 2.3: |
The Abstract Index Notation / 2.4: |
Curvature / 3: |
Derivative Operators and Parallel Transport / 3.1: |
Geodesics / 3.2: |
Methods for Computing Curvature / 3.4: |
Einstein's Equation / 4: |
The Geometry of Space in Prerelativity Physics; General and Special Covariance / 4.1: |
Special Relativity / 4.2: |
Linearized Gravity: The Newtonian Limit and Gravitational Radiation / 4.3: |
Homogeneous, Isotropic Cosmology / 5: |
Homogeneity and Isotrophy / 5.1: |
Dynamics of a Homogeneous, Isotropic Universe / 5.2: |
The Cosmological Redshift; Horizons / 5.3: |
The Evolution of Our Universe / 5.4: |
The Schwartzschild Solution / 6: |
Derivation of the Schwartzschild Solution / 6.1: |
Interior Solutions / 6.2: |
Geodesics of Schwartzschild: Gravitation Redshift, Perihelion Precession, Bending of Light, and Time Delay / 6.3: |
The Kruskal Extension / 6.4: |
Advanced Topics / Part II: |
Methods for Solving Einstein's Equation / 7: |
Stationary, Axisymmetric Solutions / 7.1: |
Spatially Homogeneous Cosmologies / 7.2: |
Algebraically Special Solutions / 7.3: |
Methods for Generating Solutions / 7.4: |
Perturbations / 7.5: |
Casual Structure / 8: |
Futures and Pasts: Basic Definitions and Results / 8.1: |
Causality Conditions / 8.2: |
Domains of Dependence; Global Hyperbolicity / 8.3: |
Singularities / 9: |
What is a Singularity? / 9.1: |
Timelike and Null Geodesic Congruences / 9.2: |
Conjugate Points / 9.3: |
Existence of Maximum Length Curves / 9.4: |
Singularity Theorems / 9.5: |
The Initial Value Formulation / 10: |
Initial Value Formulation for Particles and Fields / 10.1: |
Initial Value Formulation of General Relativity / 10.2: |
Asymptotic Flatness / 11: |
Conformal Infinity / 11.1: |
Energy / 11.2: |
Black Holes / 12: |
Black Holes and the Cosmic Censor Conjecture / 12.1: |
General Properties of Black Holes / 12.2: |
The Charged Kerr Black Holes / 12.3: |
Energy Extraction from Black Holes / 12.4: |
Black Holes and Thermodynamics / 12.5: |
Spinors / 13: |
Spinors in Minkowski Spacetime / 13.1: |
Spinors in Curved Spacetime / 13.2: |
Quantum Effects in Strong Gravitational Fields / 14: |
Quantum Gravity / 14.1: |
Quantum Fields in Curved Spacetime / 14.2: |
Particle Creation near Black Holes / 14.3: |
Black Hold Thermodynamics / 14.4: |
Appendices |
Topological Spaces / A: |
Differential Forms, Integration, and Frobenius's Theorem / B: |
Differential Forms / B.1: |
Integration / B.2: |
Frobenius's Theorem / B.3: |
Maps of Manifolds, Lie Derivatives, and Killing Fields / C: |
Maps of Manifolds / C.1: |
Lie Derivatives / C.2: |
Killing Vector Fields / C.3: |
Conformal Transformations / D: |
Lagrangian and Hamiltonian Formulations of Einstein's Equation / E: |
Lagrangian Formulation / E.1: |
Hamiltonian Formulation / E.2: |
Units and Dimensions / F: |
References |
Index |