General Theory of Relativity

Anadijiban Das, Simon Fraser University, Burnaby, British Columbia, Canada, das@sfu.ca  Andrew DeBenedictis, Simon Fraser University, Burnaby, British Columbia, Canada, adebened@sfu.ca

• 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.

From the reviews: "The book under review grew out of courses that were taught by the senior author (Das) over the years ... . it does serve as a useful reference work for researchers who would prefer a direct exposition of the topics that they are involved with." (David H. Delphenich, Mathematical Reviews, May, 2013) "This advanced work is only for those who are familiar with high-level tensor mathematics or who specialize in gravitation theory. ... The authors provide detailed proofs to theorems with elaborate discussion. ... Every chapter contains exercises with hints to solve them or complete solutions. An exhaustive list of references and a good index support the text. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals." (N. Sadanand, Choice, Vol. 50 (5), January, 2013) "The General Theory of Relativity: A Mathematical Exposition is ... written in a very clear style and the mathematics is done carefully and in detail. There are also a lot of 'examples, worked-out problems, and exercises (with hints and solutions),' ... so it is certainly a pedagogically sound enterprise well worth the price of admission. I am happy to be able to recommend it." (Michael Berg, The Mathematical Association of America, August, 2012)