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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: PrefaceNotation and ConventionsPART I. FUNDAMENTALS1. Introduction1.1 Introduction1.2 Space and Time in Prerelativity Physics and in Special Relativity1.3 The Spacetime Metric1.4 General Relativity2. Manifolds and Tensor Fields2.1 Manifolds2.2 Vectors2.3 Tensors; the Metric Tensor2.4 The Abstract Index Notation3. Curvature3.1 Derivative Operators and Parallel Transport3.2 Curvature3.3 Geodesics3.4 Methods for Computing Curvature4. Einstein's Equation4.1 The Geometry of Space in Prerelativity Physics; General and Special Covariance4.2 Special Relativity4.3 General Relativity4.4 Linearized Gravity: The Newtonian Limit and Gravitational Radiation5. Homogeneous, Isotropic Cosmology5.1 Homogeneity and Isotrophy5.2 Dynamics of a Homogeneous, Isotropic Universe5.3 The Cosmological Redshift; Horizons5.4 The Evolution of Our Universe6. The Schwartzschild Solution6.1 Derivation of the Schwartzschild Solution6.2 Interior Solutions6.3 Geodesics of Schwartzschild: Gravitation Redshift, Perihelion Precession, Bending of Light, and Time Delay6.4 The Kruskal ExtensionPART II. ADVANCED TOPICS7. Methods for Solving Einstein's Equation7.1 Stationary, Axisymmetric Solutions7.2 Spatially Homogeneous Cosmologies7.3 Algebraically Special Solutions7.4 Methods for Generating Solutions7.5 Perturbations8. Casual Structure8.1 Futures and Pasts: Basic Definitions and Results8.2 Causality Conditions8.3 Domains of Dependence; Global Hyperbolicity9. Singularities9.1 What is a Singularity?9.2 Timelike and Null Geodesic Congruences9.3 Conjugate Points9.4 Existence of Maximum Length Curves9.5 Singularity Theorems10. The Initial Value Formulation10.1 Initial Value Formulation for Particles and Fields10.2 Initial Value Formulation of General Relativity11. Asymptotic Flatness11.1 Conformal Infinity11.2 Energy12. Black Holes12.1 Black Holes and the Cosmic Censor Conjecture12.2 General Properties of Black Holes12.3 The Charged Kerr Black Holes12.4 Energy Extraction from Black Holes12.5 Black Holes and Thermodynamics13. Spinors13.1 Spinors in Minkowski Spacetime13.2 Spinors in Curved Spacetime14. Quantum Effects in Strong Gravitational Fields14.1 Quantum Gravity14.2 Quantum Fields in Curved Spacetime14.3 Particle Creation near Black Holes14.4 Black Hold ThermodynamicsAPPENDICESA. Topological SpacesB. Differential Forms, Integration, and Frobenius's TheoremB.1 Differential FormsB.2 IntegrationB.3 Frobenius's TheoremC. Maps of Manifolds, Lie Derivatives, and Killing FieldsC.1 Maps of ManifoldsC.2 Lie DerivativesC.3 Killing Vector FieldsD. Conformal TransformationsE. Lagrangian and Hamiltonian Formulations of Einstein's EquationE.1 Lagrangian FormulationE.2 Hamiltonian FormulationF. Units and DimensionsReferencesIndex
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