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General Relativity

by Robert Wald

  • ISBN: 9780226870335
  • ISBN10: 0226870332

General Relativity

by Robert Wald

  • Binding: Paperback
  • Publisher: Univ of Chicago Pr
  • Publish date: 07/01/1984
  • ISBN: 9780226870335
  • ISBN10: 0226870332
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Description: Preface Notation and Conventions PART I. FUNDAMENTALS 1. Introduction 1.1 Introduction 1.2 Space and Time in Prerelativity Physics and in Special Relativity 1.3 The Spacetime Metric 1.4 General Relativity 2. Manifolds and Tensor Fields 2.1 Manifolds 2.2 Vectors 2.3 Tensors; the Metric Tensor 2.4 The Abstract Index Notation 3. Curvature 3.1 Derivative Operators and Parallel Transport 3.2 Curvature 3.3 Geodesics 3.4 Methods for Computing Curvature 4. Einstein's Equation 4.1 The Geometry of Space in Prerelativity Physics; General and Special Covariance 4.2 Special Relativity 4.3 General Relativity 4.4 Linearized Gravity: The Newtonian Limit and Gravitational Radiation 5. Homogeneous, Isotropic Cosmology 5.1 Homogeneity and Isotrophy 5.2 Dynamics of a Homogeneous, Isotropic Universe 5.3 The Cosmological Redshift; Horizons 5.4 The Evolution of Our Universe 6. The Schwartzschild Solution 6.1 Derivation of the Schwartzschild Solution 6.2 Interior Solutions 6.3 Geodesics of Schwartzschild: Gravitation Redshift, Perihelion Precession, Bending of Light, and Time Delay 6.4 The Kruskal Extension PART II. ADVANCED TOPICS 7. Methods for Solving Einstein's Equation 7.1 Stationary, Axisymmetric Solutions 7.2 Spatially Homogeneous Cosmologies 7.3 Algebraically Special Solutions 7.4 Methods for Generating Solutions 7.5 Perturbations 8. Casual Structure 8.1 Futures and Pasts: Basic Definitions and Results 8.2 Causality Conditions 8.3 Domains of Dependence; Global Hyperbolicity 9. Singularities 9.1 What is a Singularity? 9.2 Timelike and Null Geodesic Congruences 9.3 Conjugate Points 9.4 Existence of Maximum Length Curves 9.5 Singularity Theorems 10. The Initial Value Formulation 10.1 Initial Value Formulation for Particles and Fields 10.2 Initial Value Formulation of General Relativity 11. Asymptotic Flatness 11.1 Conformal Infinity 11.2 Energy 12. Black Holes 12.1 Black Holes and the Cosmic Censor Conjecture 12.2 General Properties of Black Holes 12.3 The Charged Kerr Black Holes 12.4 Energy Extraction from Black Holes 12.5 Black Holes and Thermodynamics 13. Spinors 13.1 Spinors in Minkowski Spacetime 13.2 Spinors in Curved Spacetime 14. Quantum Effects in Strong Gravitational Fields 14.1 Quantum Gravity 14.2 Quantum Fields in Curved Spacetime 14.3 Particle Creation near Black Holes 14.4 Black Hold Thermodynamics APPENDICES A. Topological Spaces B. Differential Forms, Integration, and Frobenius's Theorem B.1 Differential Forms B.2 Integration B.3 Frobenius's Theorem C. Maps of Manifolds, Lie Derivatives, and Killing Fields C.1 Maps of Manifolds C.2 Lie Derivatives C.3 Killing Vector Fields D. Conformal Transformations E. Lagrangian and Hamiltonian Formulations of Einstein's Equation E.1 Lagrangian Formulation E.2 Hamiltonian Formulation F. Units and Dimensions References Index
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