An Introduction to General Relativity

by L. P. Hughston , K. P. Tod

• ISBN13: 9780521339438
• ISBN10: 052133943X
• eBook ISBN(s): 9781107108042
• Format: Paperback
• Copyright: 1991-01-25
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

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.