General Theory of Relativity

by Dirac, P. A. M.

• ISBN13: 9780691011462
• ISBN10: 069101146X
• Edition: Reprint
• Format: Paperback
• Copyright: 1996-01-08
• Publisher: Princeton Univ Pr

Summary

Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate,General Theory of Relativitycomprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

Author Biography

P.A.M. Dirac (1902-1984) was Lucasian Professor of Mathematics at the University of Cambridge and later taught at Florida State University.

Table of Contents

Special Relativity	p. 1
Oblique Axes	p. 3
Curvilinear Coordinates	p. 5
Nontensors	p. 8
Curved Space	p. 9
Parallel Displacement	p. 10
Christoffel Symbols	p. 12
Geodesics	p. 14
The Stationary Property of Geodesics	p. 16
Covariant Differentiation	p. 17
The Curvature Tensor	p. 20
The Condition for Flat Space	p. 22
The Bianchi Relations	p. 23
The Ricci Tensor	p. 24
Einstein's Law of Gravitation	p. 25
The Newtonian Approximation	p. 26
The Gravitational Red Shift	p. 29
The Schwarzchild Solution	p. 30
Black Holes	p. 32
Tensor Densities	p. 36
Gauss and Stokes Theorems	p. 38
Harmonic Coordinates	p. 40
The Electromagnetic Field	p. 41
Modification of the Einstein Equations by the Presence of Matter	p. 43
The Material Energy Tensor	p. 45
The Gravitational Action Principle	p. 48
The Action for a Continuous Distribution of Matter	p. 50
The Action for the Electromagnetic Field	p. 54
The Action for Charged Matter	p. 55
The Comprehensive Action Principle	p. 58
The Pseudo-Energy Tensor of the Gravitational Field	p. 61
Explicit Expression for the Pseudo-Tensor	p. 63
Gravitational Waves	p. 64
The Polarization of Gravitational Waves	p. 66
The Cosmological Term	p. 68
Index	p. 71
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