Relativity: An Introduction to Special and General Relativity

by Hans Stephani

• ISBN13: 9780521010696
• ISBN10: 0521010691
• Edition: 3rd
• Format: Paperback
• Copyright: 2004-03-29
• Publisher: Cambridge University Press

Summary

Thoroughly revised and updated, this textbook provides a pedagogical introduction to relativity. It is self-contained, but the reader is expected to have a basic knowledge of theoretical mechanics and electrodynamics. It covers the most important features of both special and general relativity, as well as touching on more difficult topics, such as the field of charged pole-dipole particles, the Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools (tensor calculus, Riemannian geometry) are provided, most of the derivations are given in full, and exercises are included where appropriate. Written as a textbook for undergraduate and introductory graduate courses, it will also be of use to researchers working in the field. The bibliography gives the original papers and directs the reader to useful monographs and review papers.

Table of Contents

Foreword

Part I. Special Relativity: 1. Introduction: inertial systems and Galilei invariance

2. Light propagation and Lorenz 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 algebraic properties of electromagnetic fields

10. Charged point particles and their field

11. Pole-dipole particles and their field

12. Electodynamics in media

13. Perfect fluids and other physical theories

Part II. Riemannian Geometry: 14. The force-free motion of particles

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 and balance equations

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 of spherically-symmetric stars

37. Rotating black holes

38. Black holes are not black

39. The conformal structure of infinity

Part VII. Cosmology: 40. Robertson-Walker metrics and their properties

41. The dynamics of R-W metrics and the Friedmann universes

42. Our Universe as a Friedmann model

43. General cosmological models

Bibliography

Index.