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Gravitation (Physics Series) by Kip S. Thorne Charles W. Misner John Archibald Wheeler

This book can be divided into three logical parts. The first part includes an overview of 4 dimensional physics (spacetime physics, chapter 1), an introduction to special relativity (physics in flat spacetime, chapters 2 to 7), an introduction to the tensor calculus (the mathematics of curved spacetime, chapters 8 to 15) and describes in detail Einstein's general theory of relativity (Einstein's geometric theory of relativity, chapters 16 to 22).

This first part is the best introduction to the theory of relativity I have ever read. The mathematics is introduced in a very comprehensive manner, there are lots of exercises where the reader can get used to the tensor calculus. The physical explanations are just brilliant and what is more important general relativity is introduced in the manner Einstein itself viewed it: as a geometric representation of gravity! Other books on this subject formulate general relativity only algebraically (like quantum theory) but this hides the importance of the idea that all gravitational effects can be extracted from the geometry of spacetime. The algebraic formulation may be regarded as more modern by some authors, it must be said however that no algebraic formulation managed to give more physical insight. The algebraic treatment tries to unify the view of general relativity and quantum field theory, but the physical discrepancies between the two theories remain unsolved.

The second part starts with the application of general relativity to stars (stars and relativity, chapters 23 to 26), goes on to the universe (the universe, chapters 27-30) and to black holes (gravitational collapse and black holes, chapters 31 to 34), and describes finally gravitational waves (gravitational waves, chapters 35 to 37) and experimental methods (experimental tests of general relativity, chapters 38 to 40).

This second part is a good overview, but many details of the computations of the applications are not shown. For the readers interrested in the details the two volume book by Zel'dovich and Novikov "Stars and Relativity"/"The Structure and Evolution of the Universe" is much better (but also much longer).

The third part finally describes the frontiers of general relativity (frontiers, chapters 41 to 44). Like part two it gives a good overview not showing many computational details.

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