Einstein's General Theory of Relativity: A Concise Introduction

Brian P. Dolan

doi:10.1017/9781009263689

Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.

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Contents

Frontmatter
pp i-iv
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Dedication
pp v-vi
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Contents
pp vii-viii
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Preface
pp ix-x
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1 - Introduction
pp 1-13
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2 - Metrics
pp 14-43
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3 - Geodesics
pp 44-84
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4 - The Geometry of Curved Spaces
pp 85-118
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5 - Einstein’s Field Equations
pp 119-125
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6 - Solutions of Einstein’s Equations in Empty Space
pp 126-138
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7 - Cosmology and the Big Bang
pp 139-176
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Appendix A - Tensors of Type (p, q)
pp 177-177
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Appendix B - The Riemann Tensor
pp 178-186
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Appendix C - The Energy-Momentum Tensor
pp 187-191
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Appendix D - The Schwarzschild Metric
pp 192-194
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Appendix E - Robertson-Walker Space-Time
pp 195-197
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References
pp 198-198
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Index
pp 199-204
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Einstein's General Theory of Relativity

A Concise Introduction

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-viii

Preface
pp ix-x

1 - Introduction
pp 1-13

2 - Metrics
pp 14-43

3 - Geodesics
pp 44-84

4 - The Geometry of Curved Spaces
pp 85-118

5 - Einstein’s Field Equations
pp 119-125

6 - Solutions of Einstein’s Equations in Empty Space
pp 126-138

7 - Cosmology and the Big Bang
pp 139-176

Appendix A - Tensors of Type (p, q)
pp 177-177

Appendix B - The Riemann Tensor
pp 178-186

Appendix C - The Energy-Momentum Tensor
pp 187-191

Appendix D - The Schwarzschild Metric
pp 192-194

Appendix E - Robertson-Walker Space-Time
pp 195-197

References
pp 198-198

Index
pp 199-204

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A Concise Introduction

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