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A clear strength of the book is that it is well-rounded, covering topics from differential geometry to applications, and from basic concepts to mathematical and physical theories. For instance, in the first chapter, the book introduces the concept of spacetime, and covers how spacetime is modeled, such as in the case of Minkowski spacetime. It then moves on to the more general case of curved spacetime, such as in the case of Schwarzschild spacetime (chapter 2). Then it discusses the gravitational field equation (chapter 3), the purpose of general relativity (chapter 4), and the theory of general relativity (chapter 5). Chapters 6 to 8 cover topics such as black holes, gravitational radiation, and cosmology. Chapters 9 to 11 discuss various topics such as the concept of local coordinate systems and curvature, and the curvature tensor and the Riemann tensor. Chapters 12 and 13 discuss topics such as general relativity in curved spaces, and gauge theories. Chapters 14 to 16 cover topics such as the Einstein field equation and cosmology.
Spacetime and Geometry: An Introduction to General Relativity is an excellent textbook for those who want to learn general relativity without the daunting notation. The book is written in a clear and accessible style with theorems and proofs clarified at the beginning of each chapter. The organization of the book is clear and logical, and the writing is concise and thorough. There is ample space to explain difficult concepts in a simple and straightforward manner, and an appendix at the end of the book contains a set of solved problems.
The book can serve as a very introductory text to general relativity, or as a companion text to Classical and Quantum Gravity: Theory and Applications (2nd Edition, B. Nolan, L. F. Abbott, and P. J. E. Peebles, Wiley-Blackwell, 2014), the classic book on general relativity. The book is well-rounded, and covers topics in relativity, geometry, and cosmology in a structured and elegant manner. The book is useful for the general reader, as well as for those who are interested in advanced undergraduates or graduate students. I would recommend it highly as a text for graduate students of physics who want a comprehensive, well-written, and elegant introduction to general relativity.
The authors have done a first-rate job of presenting a coherent account of the theory of relativity in a clear and concise style, and they have clearly made an effort to ensure that students who know less than they will find the text approachable. They have not, however, provided any real examples of calculus or special relativity in the appendices, and it is necessary for the average student to know a little bit about differential geometry before tackling the mathematics of the book. The many figures, however, are very clear and the book is well-written and easy to read.
This book has been previously published as a companion volume to Spacetime and Geometry: An Introduction to General Relativity , a Cambridge University Press textbook for undergraduates. The two books complement each other. 827ec27edc