A Short Course in General Relativity

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Springer Science & Business Media, Apr 30, 2010 - Science - 292 pages
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Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding.

The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology.

This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes – "Special Relativity Review" and "The Chinese Connection" - and outline solutions to all exercises and problems, making it especially suitable for private study.

 

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Contents

1 Vector and tensor fields
7
2 The spacetime of general relativity and paths of particles
53
3 Field equations and curvature
97
4 Physics in the vicinity of a massive object
122
5 Gravitational radiation
169
6 Elements of cosmology
183
Appendices
208
A Special relativity review
209
B The Chinese connection
233
C Tensors and Manifolds
241
Solutions
259
References
282
Index
287
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About the author (2010)

J.D. Nightingale is Emeritus Professor of Physics at the State University of New York, College at New Paltz. J. Foster is recently retired Senior Lecturer in Mathematics at the University of Sussex. Both have extensive teaching experience in applied mathematics and theoretical physics. Prof. Nightingale's research interests tend towards the physical and cosmological consequences of general relativity, while Prof. Foster's tend towards the more mathematical aspects, such as exact solutions.

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