A Short Course in General Relativity

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.

From the reviews of the third edition:

"This is the third edition of a book that is already familiar to those who teach an introductory course in general relativity. … Important concepts are introduced slowly and carefully, so that the resulting text is a comprehensible first introduction that is suitable for both physics and mathematics students. … its strength is that it is a short introduction to the subject that still covers all the essential material for a first course and provides a sound basis for further study." (J. B. Griffiths, Mathematical Reviews, Issue 2006 h)

"This book is a well-developed introduction to General Relativity. … the present third edition is really re-worked in many places in comparison with the previous ones. … Three appendices are quite helpful … . Solutions to the exercises, References and Index close this very readable book. … Every chapter ends with a list of problems … ." (Hans-Jürgen Schmidt, Zentralblatt MATH, Vol. 1089 (15), 2006)

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.