General Relativity

General Relativity


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Product Details

ISBN-13: 9780521240086
Publisher: Cambridge University Press
Publication date: 08/19/1982
Pages: 314
Product dimensions: 5.98(w) x 8.98(h) x (d)

Table of Contents

Preface; Notation;

Part I. Special Relativity:

1. Introduction: inertial systems and Galilei invariance of classical mechanics;
2. Light propagation in moving coordinate systems and Lorentz transformations;
3. Our world as a Minkowski space;
4. Mechanics of special relativity;
5. Optics of plane waves;
6. Four-dimensional vectors and tensors;
7. Electrodynamics in vacuo;
8. Transformation properties of electromagnetic fields: examples;
9. Null vectors and the algebraic properties of electromagnetic field tensors;
10. Charged point particles and their field;
11. Pole-dipole particles and their field;
12. Electrodynamics in media;
13. Perfect fluids and other physical theories;

Part II. Riemannian Geometry:
14. Introduction: the force-free motion of particles in Newtonian mechanics;
15. Why Riemannian geometry?;
16. Riemannian space;
17. Tensor algebra;
18. The covariant derivative and parallel transport;
19. The curvature tensor;
20. Differential operators, integrals and integral laws;
21. Fundamental laws of physics in Riemannian spaces;

Part III. Foundations of Einstein's Theory of Gravitation:
22. The fundamental equations of Einstein's theory of gravitation;
23. The Schwarzschild solution;
24. Experiments to verify the Schwarzschild metric;
25. Gravitational lenses;
26. The interior Schwarzschild solution;

Part IV. Linearized Theory of Gravitation, Far Fields and Gravitational Waves:
27. The linearized Einstein theory of gravity;
28. Far fields due to arbitrary matter distributions and balance equations for momentum and angularmomentum;
29. Gravitational waves;
30. The Cauchy problem for the Einstein field equations;

Part V. Invariant Characterization of Exact Solutions:
31. Preferred vector fields and their properties;
32. The Petrov classification;
33. Killing vectors and groups of motion;
34. A survey of some selected classes of exact solutions;

Part VI. Gravitational Collapse and Black Holes:
35. The Schwarzschild singularity;
36. Gravitational collapse - the possible life history of a spherically symmetric star;
37. Rotating black holes;
38. Black holes are not black - relativity theory and quantum theory;
39. The conformal structure of infinity;

Part VII. Cosmology:
40. Robertson-Walker metrics and their properties;
41. The dynamics of Robertson-Walker metrics and the Friedmann universes;
42. Our Universe as a Friedmann model;
43. General cosmological models; Bibliography; Index.

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