## A First Course in General RelativityClarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered with Schutz's characteristic ease and authority - from black holes to gravitational lenses, from pulsars to the study of the Universe as a whole. This edition now contains discoveries by astronomers that require general relativity for their explanation; a revised chapter on relativistic stars, including new information on pulsars; an entirely rewritten chapter on cosmology; and an extended, comprehensive treatment of modern detectors and expected sources. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, whilst the informal writing style makes the subject matter easily accessible. |

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### Contents

Vector analysis in special relativity | 33 |

Tensor analysis in special relativity | 56 |

Perfect fluids in special relativity | 84 |

Preface to curvature | 111 |

Curved manifolds | 142 |

Physics in a curved spacetime | 171 |

The Einstein field equations | 184 |

Gravitational radiation 2 03 | 203 |

Spherical solutions for stars | 256 |

Schwarzschild geometry and black holes | 281 |

Cosmology | 335 |

Appendix A Summary of linear algebra | 374 |

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### Common terms and phrases

acceleration amplitude angular momentum arbitrary astronomers axes axis basis vectors Big Bang binary black holes calculate called Cartesian Christoffel symbols clock components compute conservation coordinate system cosmological constant covariant curvature curve deﬁned deﬁnition deﬂection Derive Eq detectors discussion distance Einstein Einstein’s equations electromagnetic energy density ergoregion Euclidean Euclidean space Exer ﬁnd ﬁnite ﬁrst order ﬁxed ﬂat ﬂuid element ﬂux four-momentum four-velocity freely falling frequency function galaxies gauge geodesic geometry gravitational ﬁeld gravitational waves horizon inertial frame inﬁnity integral interferometers Kerr metric light linear Lorentz transformation luminosity manifold matrix MCRF measure metric tensor neutron stars notation null observer one-form orbit orthogonal parameter particle photon physics plane polar pulsars quantum radiation radius real number redshift relativistic relativity rotation satisﬁes scalar Schwarzschild Schwarzschild metric Show solution space spacetime diagram spatial speed spherical surface symmetric tangent theory timelike universe velocity world line zero