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Spacetime and geometry. An introduction to general relativity. (English) Zbl 1131.83001
San Francisco, CA: Addison Wesley (ISBN 0-8053-8732-3). xiv, 513 p. (2004).
From the preface: General relativity is the most beautiful physical theory ever invented. It describes one of the most pervasive features of the world we experience – gravitation – in terms of an elegant mathematical structure – the differential geometry of curved spacetime – leading to unambiguous predictions that have received spectacular experimental confirmation. Consequences of general relativity, from the big bang to black holes, are often what get young people first interested in physics, and it is an unalloyed joy to finally reach the point in one’s studies where these phenomena may be understood at a rigorous quantitative level. If you are contemplating reading this book, that point is here.
In recent decades, general relativity (GR) has become an integral and indispensable part of modern physics. For a long time after it was proposed by Einstein in 1916, GR was counted as a shining achievement that lay somewhat outside the mainstream of interesting research. Increasingly, however, contemporary students in a variety of specialties are finding it necessary to study Einstein’s theory. In addition to being an active research area in its own right, GR is part of the standard syllabus for anyone interested in astrophysics, cosmology, string theory, and even particle physics. This is not to slight the more pragmatic uses of GR, including the workings of the Global Positioning System (GPS) satellite network.
There is no shortage of books on GR, and many of them are excellent. Indeed, approximately thirty years ago witnessed the appearance of no fewer than three books in the subject, each of which has become a classic in its own right: those by Weinberg (1972), Misner, Thorne, and Wheeler (1973), and Hawking and Ellis (1975). Each of these books is suffused with a strongly-held point of view advocated by the authors. This has led to a love-hate relationship between these works and their readers; in each case, it takes little effort to find students who will declare them to be the best textbook ever written, or other students who find them completely unpalatable. For the individuals in question, these judgments may very well be correct; there are many different ways to approach this subject.
The present book has a single purpose: to provide a clear introduction to general relativity, suitable for graduate students or advanced undergraduates. I have attempted to include enough material so that almost any one-semester introductory course on GR can find the appropriate subjects covered in the text, but not too much more than that. In particular, I have tried to resist the temptation to write a comprehensive reference book. The only goal of this book is to teach you GR.”
Contents: 1. Special relativity and flat spacetime; 2. Manifolds; 3. Curvature; 4. Gravitation; 5. The Schwarzschild solution; 6. More general black holes; 7. Perturbation theory and gravitational radiation; 8. Cosmology; 9. Quantum field theory in curved spacetime.

83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory
53C80 Applications of global differential geometry to the sciences
83Cxx General relativity
83C57 Black holes
83F05 Cosmology