General Theory of RelativityEinstein'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. |
Contents
Special Relativity | 1 |
Oblique Axes | 3 |
Curvilinear Coordinates | 5 |
Nontensors | 8 |
Curved Space | 9 |
Parallel Displacement | 10 |
Christoffel Symbols | 12 |
Geodesics | 14 |
Tensor Densities | 36 |
Gauss and Stokes Theorems | 38 |
Harmonic Coordinates | 40 |
The Electromagnetic Field | 41 |
Modification of the Einstein Equations by the Presence of Matter | 43 |
The Material Energy Tensor | 45 |
The Gravitational Action Principle | 48 |
The Action for a Continuous Distribution of Matter | 50 |
The Stationary Property of Geodesics | 16 |
Covariant Differentiation | 17 |
The Curvature Tensor | 20 |
The Condition for Flat Space | 22 |
The Bianci Relations | 23 |
The Ricci Tensor | 24 |
Einsteins Law of Gravitation | 25 |
The Newtonian Approximation | 26 |
The Gravitational Red Shift | 29 |
The Schwarzchild Solution | 30 |
Black Holes | 32 |
The Action for the Electromagnetic Field | 54 |
The Action for Charged Matter | 55 |
The Comprehensive Action Principle | 58 |
The PseudoEnergy Tensor of the Gravitational Field | 61 |
Explicit Expression for the PseudoTensor | 63 |
Gravitational Waves | 64 |
The Polarization of Gravitational Waves | 66 |
The Cosmological Term | 68 |
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Common terms and phrases
A₁ Bianci relation change of coordinates charged matter Christoffel symbol coefficient components condition conservation constant contravariant vector coordinate system covariant derivative covariant differentiation covariant vector curved space curvilinear coordinates d'Alembert equation dªx denote distribution of matter downstairs suffix dr² ds² dx¹ dx² dx³ Einstein equations Einstein's law electromagnetic field empty space energy and momentum equations for empty field equations field quantity flat space formula four-dimensional function gaß geodesic gives gravitational field gravitational waves harmonic coordinates Hence integral invariant Let us take lower suffixes material energy tensor multiply Newtonian approximation nontensor number of dimensions oblique axes parallel displacement particle physical pseudo-tensor result Ricci tensor right-hand side Schwarzschild solution Section shift sin² special relativity static surface symmetrical system of coordinates TENSOR DENSITIES term theorem timelike transform upstairs values vanishes world line μα μν μν μν μν,σ ду