General Theory of Relativity

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Princeton University Press, Aug 10, 2016 - Science - 80 pages

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 Relativity comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

 

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Contents

1 Special Relativity
1
2 Oblique Axes
3
3 Curvilinear Coordinates
5
4 Nontensors
8
5 Curved Space
9
6 Parallel Displacement
10
7 Christoffel Symbols
12
8 Geodesics
14
20 Tensor Densities
36
21 Gauss and Stokes Theorems
38
22 Harmonic Coordinates
40
23 The Electromagnetic Field
41
24 Modification of the Einstein Equations by the Presence of Matter ...
43
25 The Material Energy Tensor
45
26 The Gravitational Action Principle
48
27 The Action for a Continuous Distribution of Matter ...
50

9 The Stationary Property of Geodesics
16
10 Covariant Differentiation
17
11 The Curvature Tensor
20
12 The Condition for Flat Space
22
13 The Bianci Relations
23
14 The Ricci Tensor
24
15 Einsteins Law of Gravitation
25
16 The Newtonian Approximation
26
17 The Gravitational Red Shift
29
18 The Schwarzchild Solution
30
19 Black Holes
32
28 The Action for the Electromagnetic Field
54
29 The Action for Charged Matter
55
30 The Comprehensive Action Principle
58
31 The PseudoEnergy Tensor of the Gravitational Field ...
61
32 Explicit Expression for the PseudoTensor
63
33 Gravitational Waves
64
34 The Polarization of Gravitational Waves
66
35 The Cosmological Term
68
Index
71
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About the author (2016)

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

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