## A Short Course in General RelativitySuitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding. The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology. This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes – "Special Relativity Review" and "The Chinese Connection" - and outline solutions to all exercises and problems, making it especially suitable for private study. |

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### Contents

1 Vector and tensor fields | 7 |

2 The spacetime of general relativity and paths of particles | 53 |

3 Field equations and curvature | 97 |

4 Physics in the vicinity of a massive object | 122 |

5 Gravitational radiation | 169 |

6 Elements of cosmology | 183 |

Appendices | 208 |

A Special relativity review | 209 |

B The Chinese connection | 233 |

C Tensors and Manifolds | 241 |

Solutions | 259 |

References | 282 |

Index | 287 |