General Relativity

Product Description "Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

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

About the Author Robert M. Wald is professor in the Department of Physics and the Enrico Fermi Institute at the University of Chicago. He is the author of Space, Time, and Gravity: The Theory of the Big Bang and Black Holes, also published by the University of Chicago Press.

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