The General Theory of Relativity: A Mathematical Exposition

Tensor Analysis on Differentiable Manifolds.- The Pseudo-Riemannian Space-Time Manifold M4.- Spherically Symmetric Space-Time Domains.- Static and Stationary Space-Time Domains.- Black Holes.- Cosmology.- Algebraic Classification of Field Equations.- The Coupled Einstein-Maxwell-Klein-Gordon Equations.- Appendix 1: Variational Derivation of Differential Equations.- Appendix 2: Partial Differential Equations.- Appendix 3: Canonical Forms of Matrices.- Appendix 4: Conformally Flat Space-Times and "the Fifth Force".- Appendix 5: Linearized Theory and Gravitational Waves.- Appendix 6: Exotic Solutions: Wormholes, Warp-Drives, and Time Machines.- Appendix 7: Gravitational Instantons.- Appendix 8: Computational Symbolic Algebra Calculations.- References.- Index of Symbols.- Index.