General Relativity
9780226870335
9780226870373
General Relativity
A classic textbook designed to help students understand general relativity
Robert M. Wald's book has been a staple of physics teaching for decades. It offers straightforward, rigorous analyses of current understandings of all the central questions and problems of the field, giving each the complexity it requires while making every effort to keep the whole accessible to a student who is embarking on the study of this subject for the first time.
Robert M. Wald's book has been a staple of physics teaching for decades. It offers straightforward, rigorous analyses of current understandings of all the central questions and problems of the field, giving each the complexity it requires while making every effort to keep the whole accessible to a student who is embarking on the study of this subject for the first time.
506 pages | 6-1/2 x 9-1/4 | © 1984
Physical Sciences: Astronomy and Astrophysics, Physics and Astronomy, Theoretical Physics
Reviews
Table of Contents
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
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