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General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this 2006 book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.
1. How the theory of relativity came into being (a brief historical sketch)
Part I. Elements of Differential Geometry
2. A short sketch of two-dimensional differential geometries
3. Tensors, tensor densities
4. Covariant derivatives
5. Parallel transport and geodesic lines
6. Curvature of a manifold: flat manifolds
7. Riemannian geometry
8. Symmetries of Rieman spaces, invariance of tensors
9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs
10. The spatially homogeneous Bianchi-type spacetimes
11. The Petrov classification by the spinor method
Part II. The Gravitation Theory
12. The Einstein equations and the sources of a gravitational field
13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory
14. Spherically symmetric gravitational field of isolated objects
15. Relativistic hydrodynamics and thermodynamics
16. Relativistic cosmology I: general geometry
17. Relativistic cosmology II: the Robertson-Walker geometry
18. Relativistic cosmology III: the Lemaitre-Tolman geometry
19. Relativistic cosmology IV: generalisations of L-T and related geometries
20. The Kerr solution
21. Subjects omitted in this book
References
"In the time-honoured tradition of many books from CUP, An Introduction to General Relativity and Cosmology cannot really be described as an introduction at all. [...] an excellent high-level textbook that includes a number of topics that are not readily to be found elsewhere. I recommend it very highly for students who have studied General Relativity already (perhaps having read a real 'introductory' book), and who would like to gain a deeper mathematical insight into the subject. [...] For anyone looking for a thorough mathematical treatment of General Relativity, or for a supplement to existing books, this is highly recommended. It is not a standard text by any means, but I would be surprised if there was anyone who didn't find in it something new, interesting, and enlightening."
- The Observatory
