An Introduction to General Relativity

L. P. Hughston (Author), K. P. Tod (Author)

9780521339438, Cambridge University Press

Paperback, published 25 January 1991

192 pages, 32 b/w illus.
23 x 15.3 x 1.4 cm, 0.29 kg

"...very readable...more emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition." Quarterly of Applied MAthematics, Brown University

This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.

Preface
1. Introduction
2. Vectors and tensors in flat three-space
3. Aspects of special relativistic geometry
4. Tensor analysis on manifolds
5. Covariant differentiation
6. Properties of the Riemann tensor
7. Riemannian geometry
8. The Lie derivative
9. Geodesics
10. Geodesic deviation
11. Differential forms
12. The transition from Newtonian theory
13. Einstein's field equations
14. The slow motion approximation
15. The Schwarzschild solution
16. Gravitational red-shift and time dilation
17. The geodesic equation for the Schwarzschild solution
18. Classical tests
19. The extended Schwarzschild solution
20. Black holes and gravitational collapse
21. Interior solutions
22. The Kerr solution
23. Homogeneous and isotropic three-spaces
24. Cosmology: kinematics
25. Cosmology: dynamics
25. Anisotropic cosmologies
Index.

Subject Areas: Applied mathematics [PBW]