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The foundations are thoroughly developed together with the required mathematical background from differential geometry developed in Part III.

The author also discusses the tests of general relativity in detail, including binary pulsars, with much space is devoted to the study of compact objects, especially to neutron stars and to the basic laws of black-hole physics.

This well-structured text and reference enables readers to easily navigate through the various sections as best matches their backgrounds and perspectives, whether mathematical, physical or astronomical.

Very applications oriented, the text includes very recent results, such as the supermassive black-hole in our galaxy and first double pulsar system

General Relativity: With Applications to Astrophysics

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.