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Introducing Einstein’s relativity. (English) Zbl 0776.53046
Oxford: Clarendon Press,. xi, 383 p. (1992).
The author’s main objectives for this book are formulated by himself as follows: First of all, he wants the reader to gain insight into, and confidence in handling, the basic equations of Einstein’s relativity. In addition to this he wants to develop the course in such a way that it would be possible to reach three major topics of current interest, black holes, gravitational waves, and cosmology. From the reviewer’s point of view the author has reached these goals successfully, combining an intuitive and motivating presentation with mathematical precision where the latter is needed. Extremely helpful are more than 200 figures, illustrating subjects which in many cases are difficult to imagine.
The book grew out of a course which originally was designed for undergraduate students, but subsequently developed in depth and coverage to a level which also is suitable for postgraduate students. The parts on the undergraduate level provide a self-contained introduction to general relativity. For a better reading the higher-level parts which can be skipped for the general understanding, are marked by a bar alongside the corresponding section. Clearly, as it is the case with most textbooks including a lot of mathematical theory, the reader is assumed to solve a lot of exercises for a better understanding of the subject.
The contents of this book include 6 major parts. The first one gives a comprehensive introduction to special relativity, including elements of relativistic mechanics. The second one deals with mathematical preliminaries: tensor algebra, tensor calculus, and a short course in differential geometry. The main topics of general relativity are presented in part C: the principles of general relativity, the field equations, a variational approach to the theory, energy-momentum tensors, and the Schwarzschild solution. A detailed exposition of the different types of black holes can be found in part \(D\) while the subsequent part deals with the two main aspects of gravitational waves; plane gravitational waves, and radiation from an isolated source. The final part on cosmology covers a discussion of classical cosmological models as well as several hints to problems which are of interest for current research in this area.
In the reviewer’s opinion this book is one of the best pedagogical approaches to introduce general relativity and to present a connection to more advanced topics in this field. Hence it is highly recommendable for every student or teacher interested in this subject.

53Z05 Applications of differential geometry to physics
83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83F05 Relativistic cosmology