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Introduction

Part of the Progress in Mathematical Physics book series (PMP, volume 56)

Abstract

General Theory of Relativity (or General Relativity) is Einstein’s theory of gravitation given by him in 1915. The name also applies to its later developments. According to the theory spacetime is a Riemannian space whose metric g μν determines the gravitational field1. The Einstein equation
$$ R_{\mu \nu } - \frac{1} {2}g_{\mu \nu } R = \frac{{8\pi G}} {2}T_{\mu \nu } $$
(1.1)
governs the gravitational field. In this equation the quantities R μν, R are functions of the metric g μν and its various derivatives and T μν on the right-hand side are determined by distribution of matter.

Keywords

Black Hole Gravitational Potential Proper Time Inertial Frame Lorentz Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

Original Papers

  1. Lorentz, Einstein, Minkowski and Weyl , Principle of Relativity, Dover books, 1952 A collection of original papers on special and general theory of relativity in English translation with notes by A. Sommerfeld.Google Scholar
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Historical Matter

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Texts

  1. Albert Einstein, Meaning of Relativity, Indian Edition by Oxford Book Company, 1965 These are Einstein’s 1921 Princeton lectures, originally published by The Princeton University Press. Every student of relativity should read these 100 odd pocket-book sized pages for the clarity and brevity of the man who discovered the theory. The available editions have appendices containing Einstein’s later unified theories, none of which seem relevant today. But who knows?Google Scholar
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  23. James B. Hartle, Gravity, Pearson Education, 2002 Written in the spirit of Misner, Thorne, Wheeler, this is the best recent treatment of general relativity available to the advanced undergraduate student. The book is complete with all the exciting experimental data up to the end of the 20th century. This book is a must for every beginner.Google Scholar
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Important Reviews and Internet Sources

  1. S. W. Hawking and W. Israel, Einstein Centenary Survey, Cambridge University Press, 1979Google Scholar
  2. S. W. Hawking and W. Israel, 300 Years of Gravitation, Cambridge University Press, 1987Google Scholar
  3. Living Reviews on Relativity: (http://relativity.livingreviews.org/) An internet source of reviews which are periodically updated. In addition there are research articles and reviews available on (http://arxiv.org/) in the “gr-qc” (general relativity and quantum cosmology) section.Google Scholar

Books on Mathematics

  1. For the convenience of a physics student all texts on the general theory of relativity do try to give an introduction to Riemannian geometry with varying degrees of pedagogical attention or success. B. F. Schutz, Geometrical Methods in Mathematical Physics, Cambridge University Press, 1980 An introduction to geometry and topology used in gravity and gauge theories.Google Scholar
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  6. F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, 1983 A more advanced introduction.Google Scholar
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  9. N. J. Hicks, Notes on Differential Geometry, Von Nostrand, 1965 This is an all-time favourite. A slim, 175 page book which introduces Riemannian geometry through hypersurfaces and theorema egregium.Google Scholar

Books on Astrophysics and Cosmology

  1. Astrophysics and Cosmology are two important branches of physics where general theory of relativity is applied. The subject of cosmology has been in very rapid growth in the last ten years. T. Padmanabhan, Theoretical Astrophysics, Cambridge University Press, Vol. I, 2000, vol. II, 2001, Vol. III, 2002 This is a thorough introduction in three volumes.Google Scholar
  2. J. V. Narlikar, An Introduction to Cosmology, Cambridge University Press, 2002 For cosmology there are many recent texts but as introduction, this is perhaps the best. It gives a clear, detailed, account of all concepts with their historical background.Google Scholar
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  4. V. Mukhanov, Physical Foundations of Cosmology, Cambridge University Press, 2005 These are two of the many recent textbooks on cosmology.Google Scholar
  5. S. Weinberg, Cosmology, Oxford, 2008. A very recent advanced book on Cosmology.Google Scholar

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