General Relativity (book)

1984 graduate textbook by Robert M. Wald

General Relativity

Hardcover edition

Author| Robert Wald
Cover artist| René Magritte
Language| English
Subject| General relativity
Genre| Non-fiction
Publisher| The University of Chicago Press

Publication date

| 1984
Publication place| United States of America
Media type| Print; EPUB and PDF in 2010
Pages| xiii + 491
ISBN| 0-226-87033-2
OCLC| 10018614

Dewey Decimal

| 530.1/1 19
LC Class| QC173.6 .W35 1984

General Relativity is a graduate textbook and reference on Albert Einstein's general theory of relativity written by the gravitational physicist Robert Wald.

## Overview

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Published by the University of Chicago Press in 1984, the book, of almost 500 pages, covers many aspects of the general theory of relativity. It is divided into two parts. Part I covers the fundamentals of the subject and Part II the more advanced topics such as causal structure, and quantum effects.[1] The book uses the abstract index notation for tensors.[2] It treats spinors, the variational-principle formulation, the initial-value formulation, (exact) gravitational waves, singularities, Penrose diagrams, Hawking radiation, and black-hole thermodynamics.[3]

It is aimed at beginning graduate students and researchers.[3][1]: Preface To this end, most of the materials in Part I is geared towards an introductory course on the subject while Part II covers a wide range of advanced topics for a second term or further study. The essential mathematical methods for the formulation of general relativity are presented in Chapters 2 and 3 while more advanced techniques are discussed in Appendices A to C. Wald believes that this is the best way forward because putting all the mathematical techniques at the beginning of the book would prove to be a major obstruction for students while developing these mathematical tools as they get used would mean they are too scattered to be useful. While the Hamiltonian formalism is often presented in conjunction with the initial-value formulation, Wald's coverage of the latter is independent of the former, which is thus relegated to the appendix, alongside the Lagrangian formalism.[1]: Preface

This book uses the  − + + + {\displaystyle -+++} sign convention for reasons of technical convenience, with one important exception: in Chapter 13, only, the sign convention is switched to  + − − − {\displaystyle +
} because it is easier to treat spinors this way, and this is the most common sign convention used in the literature.[1]: Notation and Conventions

Most of the book uses geometrized units, meaning the fundamental natural constants  G {\displaystyle G} (Newton's gravitational constant) and  c {\displaystyle c} (the speed of light in vacuum) are set equal to one, except when predictions that can be tested are made.[1]: Notation and Conventions

## Table of contents

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General relativity

G μ ν + Λ g μ ν = κ T μ ν {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}

* Introduction
*     * History
* Timeline
* Tests

* Mathematical formulation

Fundamental concepts

* Equivalence principle
* Special relativity
* World line
* Pseudo-Riemannian manifold

Phenomena

* Kepler problem
* Gravitational lensing
* Gravitational redshift
* Gravitational time dilation
* Gravitational waves
* Frame-dragging
* Geodetic effect
* Event horizon
* Singularity
* Black hole

Spacetime

* Spacetime diagrams
* Minkowski spacetime
* Einstein–Rosen bridge

* Equations
* Formalisms

|  Equations

* Linearized gravity
* Einstein field equations
* Friedmann
* Geodesics
* Mathisson–Papapetrou–Dixon
* Hamilton–Jacobi–Einstein
* Raychaudhuri

Formalisms

* ADM
* BSSN
* Post-Newtonian

Advanced theory

* Kaluza–Klein theory
* Quantum gravity

Solutions

* Schwarzschild (interior)
* Reissner–Nordström
* Einstein–Rosen waves
* Wormhole
* Gödel
* Kerr
* Kerr–Newman
* Kerr–Newman–de Sitter
* Kasner
* Lemaître–Tolman
* Taub–NUT
* Milne
* Robertson–Walker
* Oppenheimer–Snyder
* pp-wave
* van Stockum dust
* Hartle–Thorne
* Vaidya
* Peres
* De Sitter-Schwarzschild
* McVittie
* Weyl
* Kerr-Newman-de-Sitter

Scientists

* Einstein
* Lorentz
* Hilbert
* Poincaré
* Schwarzschild
* de Sitter
* Reissner
* Nordström
* Weyl
* Eddington
* Friedmann
* Milne
* Zwicky
* Lemaître
* Oppenheimer
* Gödel
* Wheeler
* Robertson
* Bardeen
* Walker
* Kerr
* Chandrasekhar
* Ehlers
* Penrose
* Hawking
* Raychaudhuri
* Taylor
* Hulse
* van Stockum
* Taub
* Newman
* Yau
* Thorne
* others

* Physics portal
* Category

* v
* t
* e

* Part I: Fundamentals

* Chapter 1: Introduction
* Chapter 2: Manifolds and Tensor Fields
* Chapter 3: Curvature
* Chapter 4: Einstein's Equation
* Chapter 5: Homogeneous, Isotropic Cosmology
* Chapter 6: The Schwarzschild Solution

* Part II: Advanced Topics

* Chapter 7: Methods for Solving Einstein's Equation
* Chapter 8: Causal Structure
* Chapter 9: Singularities
* Chapter 10: Initial Value Formulation
* Chapter 11: Asymptotic Flatness
* Chapter 12: Black Holes
* Chapter 13: Spinors
* Chapter 14: Quantum Effects in Strong Gravitational Fields

* Appendices

* A. Topological Spaces
* B. Differential Forms, Integration, and Frobenius's Theorem
* C. Maps of Manifolds, Lie Derivatives, and Killing Fields
* D. Conformal Transformations
* E. Lagrangian and Hamiltonian Formulations of Einstein's Equation
* F. Units and Dimensions.

* References
* Index

## Assessment

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According to Daniel Finley, a professor at the University of New Mexico, writing in 2018, this textbook offers good physics intuition. However, the author did not use the most modern mathematical methods available, and his treatment of cosmology had become outdated. Finley considers that the abstract index notation is difficult to learn, though convenient for those who have mastered it.[2]

Theoretical physicist James W. York wrote in 1987 that General Relativity was a sophisticated yet concise book on the subject that should be appealing to the mathematically inclined, as a high level of rigor is maintained throughout the book. However, he considered that the material on linearized gravity was too short, and recommended Gravitation by Charles Misner, Kip Thorne, and John Archibald Wheeler, and Gravitation and Cosmology by Steven Weinberg as supplements.[4]

Hans C. Ohanian, who taught and researched gravitation at the Rensselaer Polytechnic Institute, considered in 1985 that General Relativity provided a modern introduction to the subject with emphasis on tensor and topological methods and offers some "sharp insights." However, its quality is very variable. Topics such as geodetic motion in the Schwarzschild metric, the Krushkal extension, and energy extraction from black holes, are handled well while empirical tests of Einstein's theory are barely scratched and the treatment of advanced topics, including cosmology, is just too brief to be useful to students. Due to its heavy use of higher mathematics, it may not be suitable for an introductory course.[5]

Lee Smolin said in 1986 that General Relativity bridges the gap between the presentation of the material in older textbooks and the literature. For example, while the early pioneers of the subject, including Einstein himself, employed coordinate-based methods, researchers since the mid-1960s had switched to coordinate-free formulations, on which Wald's text is entirely based. Its style is uniformly clear and economic, if too brief at times. Topics that deserve more attention include gravitational radiation and cosmology. However, this book could be supplemented by those by Misner, Thorne, and Wheeler, and by Weinberg. Smolin was teaching a course on general relativity to undergraduates as well as graduate students at Yale University using this book, and felt satisfied with the results. He also found it useful as a reference to refresh his memory.[6]

## See also

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* Books portal
* Physics portal

* List of books on general relativity
* Gravitation (textbook)
* Einstein Gravity in a Nutshell (textbook)
* Classical Mechanics (textbook)
* Classical Electrodynamics (textbook)

## References

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1. ^ a b c d e Wald, Robert M. General Relativity. University of Chicago Press. Printed (1980) ISBN 0-226-87033-2 (paperback), ISBN 0-226-87032-4 (hardcover); EPUB and PDF (2010) ISBN 978-0-226-87037-3
2. ^ a b A Listing of Technical Books for General Relativity. Daniel Finley. Department of Physics and Astronomy, University of New Mexico. April 1, 2018. Accessed January 18, 2019.
3. ^ a b A Guide to Relativity Books. John C. Baez et al. University of California, Riverside. September 1998. Accessed January 18, 2019.
4. ^ York, James (May 1987). "Review: General Relativity". Books. Physics Today. 40 (5). American Institute of Physics: 94–95\. Bibcode:1987PhT....40e..94W. doi:10.1063/1.2820032.
5. ^ Ohanian, Hans (September 1985). "General Relativity". Book Reviews. American Journal of Physics. 53 (9). Association of American Physics Teachers: 923–4\. Bibcode:1985AmJPh..53..923W. doi:10.1119/1.14379.
6. ^ Smolin, Lee (January–February 1986). "Review: General Relativity by Robert Wald". American Scientist. 74 (1): 82. JSTOR 27853954.

## Further reading

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* Carroll, Sean M (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley. ISBN 978-1108488396.
* Poisson, Eric (2004). A Relativist's Toolkit, The Mathematics of Black-Hole Mechanics. Cambridge University Press. ISBN 978-0521830911.
* Will, Clifford M.; Poisson, Eric (2014). Gravity: Newtonian, Post-Newtonian, Relativistic. Cambridge University Press. ISBN 978-1107032866.

## External links

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* Official University of Chicago Press website

*[OCLC]: Online Computer Library Center number
*[LC Class]: Library of Congress Classification
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