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This book provides all the necessary mathematics and also the foundations of Einstein's theory; this makes it quite different from other monographs on Relativistic Astrophysics
This text provides a comprehensive and timely introduction to general relativity. The foundations of the theory in Part I are thoroughly developed together with the required mathematical background from differential geometry in Part III. The six chapters in Part II are devoted to tests of general relativity and to many of its applications. Binary pulsars are studied in considerable detail. Much space is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and derivations of the basic laws of black hole physics. The final chapter of this part contains Witten's proof of the positive energy theorem.
The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for string theory and other fields of physics, classical as well as quantum.
Content Level »Graduate
Keywords »EFE - Gravity - RMS - Relativity - SR - astrophysics - general relativity
1 Physics in External Gravitational Fields.- 2 Einstein’s Field Equations.- 3 The Schwarzschild Solution and Classical Tests of General Relativity.- 4 Weak Gravitational Fields.- 5 The Post-Newtonian Approximation.- 6 White Dwarfs and Neutron Stars.- 7 Black Holes.- 8 The Positive Mass Theorem.- 9 Differentiable Manifolds.- 10 Tangent Vectors, Vector and Tensor Fields.- 11 The Lie Derivative.- 12 Differential Forms.- 13 Affine Connections.- 14 Some Details.- A Fundamental Equations for Hypersurfaces.- B Ricci Curvature of Warped Products.- C Frobenius Integrability Theorem.- D Collection of Important Formulas.- References.