General Relativity

by Wald, Robert M.

• ISBN13: 9780226870335
• ISBN10: 0226870332
• Format: Paperback
• Copyright: 1984-06-15
• Publisher: Univ of Chicago Pr

Summary

"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

Author Biography

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.

Table of Contents

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.