Exact space-times in Einstein's general relativity (Englisch)

2009

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Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics

1. Introduction -- 2. Basic tools and concepts -- 3. Minkowski space-time -- 4. de Sitter space-time -- 5. Anti-de Sitter space-time -- 6. Friedmann-Lemaitre-Robertson-Walker space-times -- 7. Electrovacuum and related background space-times -- 8. Schwarzschild space-time -- 9. Space-times related to Schwarzschild -- 10. Static axially symmetric space-times -- 11. Rotating black holes -- 12. Taub-NUT space-time -- 13. Stationary, axially symmetric space-times -- 14. Accelerating black holes -- 15. Further solutions for uniformly accelerating particles -- 16. Plebanski-Demianski solutions -- 17. Plane and pp-waves -- 18. Kundt solutions -- 19. Robinson-Trautman solutions -- 20. Impulsive waves -- 21. Colliding plane waves -- 22. Final miscellany -- App. A. 2-spaces of constant curvature -- App. B. 3-spaces of constant curvature