An Introduction to General Relativity and Cosmology

by Jerzy Plebanski, Andrzej Krasinski

Overview

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 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. Many topics are included that are not found in other textbooks.

Product Details

ISBN-13:	9781107407367
Publisher:	Cambridge University Press
Publication date:	09/13/2012
Edition description:	New Edition
Pages:	558
Product dimensions:	6.69(w) x 9.61(h) x 1.14(d)

About the Author

Jerzy Plebański (1928–2005) was a Polish theoretical physicist best known for his extensive research into general relativity, nonlinear electrodynamics and mathematical physics. He split his time between Warsaw, Poland, and Mexico, his permanent residence from the mid-1970s onwards. He is remembered, among other things, for defining the algebraic classification of the tensor of matter, for finding new solutions of the Einstein equations (for example, the Plebański–Demiański metric), formulation of the heavenly equations and the effective field theory relating GR and supergravity, known as Plebański action. The first part of the book is developed from Plebański's lecture notes.

Andrzej Krasiński is Emeritus Professor at the Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences in Warsaw. He served for many years on the Editorial Board of the journal 'General Relativity and Gravitation' and has acted as Poland's elected representative on the international committee of the International Society for General Relativity and Gravitation. He is author of Inhomogeneous Cosmological Models (Cambridge, 1997), co-author of Structures in the Universe by Exact Methods (Cambridge, 2009), and co-editor of Golden Oldies in General Relativity (Springer, 2013). His research record includes many papers on the interpretation of inhomogeneous cosmological models. He is also a co-author of a computer program, Ortocartan, for algebraic calculations in general relativity.

Table of Contents

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 Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.

Editorial Reviews

...an excellent high-level textbook that includes a number of topics that are not to be readily found elsewhere. I recommend it very highly for students who have studied General Relativity already... and who would like to gain a deeper mathematical insight into the subject.
Alan Heavens, The Observatory

"... A fairly comprehensive treatise in the field of relativity and cosmology. It covers topics seldom or never seen in textbooks of this kind and is therefore valuable for researchers."
Sigbjorn Hervik, Mathematical Reviews

"... an impressive and coherent account of many aspects of contemporary General Relativity theory."
Contemporary Physics

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