An Introduction to General Relativity

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Paperback | 1 April 1991

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192 Pages

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This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.

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"...the authors guide the novice along a careful, well-planned route that provides a pleasing balance between the demands of the mathematics and those of the physics." Mathematical Reviews "...very readable...more emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition." Quarterly of Applied MAthematics, Brown University

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Non-Fiction Science Physics Relativity Physics Mathematics Applied Mathematics

Introduction	p. 1
Vectors and tensors in flat three-space	p. 10
Aspects of special relativistic geometry	p. 24
Tensor analysis on manifolds	p. 46
Covariant differentiation	p. 53
Properties of the Riemann tensor	p. 57
Riemannian geometry	p. 62
The Lie derivative	p. 67
Geodesics	p. 71
Geodesic deviation	p. 76
Differential forms	p. 85
The transition from Newtonian theory	p. 92
Einstein's field equations	p. 96
The slow-motion approximation	p. 101
The Schwarzschild solution	p. 104
Gravitational red-shift and time dilation	p. 109
The geodesic equation for the Schwarzschild solution	p. 112
Classical tests	p. 117
The extended Schwarzschild solution	p. 126
Black holes and gravitational collapse	p. 133
Interior solutions	p. 137
The Kerr solution	p. 142
Homogeneous and isotropic three-spaces	p. 151
Cosmology: kinematics	p. 155
Cosmology: dynamics	p. 163
Anisotropic cosmologies	p. 170
Index	p. 180
Table of Contents provided by Syndetics. All Rights Reserved.

An Introduction to General Relativity

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Paperback

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