by Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers and Eduard Herlt, Cambridge University Press. Hardback ISBN 9780521461368, £107 ($208). Paperback ISBN 9780521467025 £50 ($94.99). E-book ISBN 9780511059179 $140.
Soon after Einstein formulated his relativistic theory of gravitation – general relativity – two of the most celebrated solutions where found: the Schwarschild solution, describing the gravitational field outside a spherically symmetric, static body, in 1915 about a month after the publication of Einstein’s work; and the Friedmann solutions in 1922 and 1924, which provide the basics of modern cosmology. Since then, in the nearly 100 years that have elapsed, thousands of solutions have been found.
Trying to enter, unguided, into the world of exact solutions is a formidable task. It is great news that this classic monograph has been re-edited in expanded form (the first edition dates from 1980). The authors have gone through the herculean job of looking at 4000 new papers since the first edition with a cut off at the end of 1999. Five new chapters have been added, and many of the previous ones have been substantially rewritten.
The book provides an excellent introduction to the mathematical structure of general relativity, and it is a useful companion to any regular course in the subject. The authors have concentrated on solutions to vacuum space–times, Einstein-Maxwell and perfect fluids. They describe in great detail the known solutions, possible equivalences, algebraic classifications, solution-generating methods etc. The exposition is always clear and elegant. It contains a thorough presentation of space–times with different groups of motion. We should be thankful to the authors for having undertaken this project. The second edition, like the first one, is a real masterpiece.
