## A First Course in General RelativityGeneral relativity has become one of the central pillars of theoretical physics, with important applications in both astrophysics and high-energy particle physics, and no modern theoretical physicist's education should be regarded as complete without some study of the subject. This textbook, based on the author's own undergraduate teaching, develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth. It reinforces this understanding by making a detailed study of the theory's most important applications - neutron stars, black holes, gravitational waves, and cosmology - using the most up-to-date astronomical developments. The book is suitable for a one-year course for beginning graduate students or for undergraduates in physics who have studied special relativity, vector calculus, and electrostatics. Graduate students should be able to use the book selectively for half-year courses. |

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### Contents

II | 1 |

III | 4 |

IV | 5 |

V | 6 |

VI | 7 |

VII | 10 |

VIII | 15 |

IX | 18 |

LVII | 151 |

LVIII | 154 |

LIX | 160 |

LX | 163 |

LXI | 167 |

LXII | 173 |

LXIII | 175 |

LXIV | 176 |

X | 24 |

XI | 25 |

XII | 26 |

XIII | 27 |

XIV | 28 |

XV | 30 |

XVI | 36 |

XVIII | 39 |

XIX | 44 |

XX | 45 |

XXI | 47 |

XXII | 50 |

XXIII | 52 |

XXIV | 53 |

XXV | 54 |

XXVI | 60 |

XXVIII | 61 |

XXIX | 62 |

XXX | 71 |

XXXI | 73 |

XXXII | 77 |

XXXIII | 78 |

XXXIV | 80 |

XXXV | 81 |

XXXVII | 89 |

XXXIX | 90 |

XL | 94 |

XLI | 97 |

XLII | 99 |

XLIII | 106 |

XLIV | 110 |

XLV | 111 |

XLVI | 112 |

XLVII | 113 |

XLVIII | 118 |

XLIX | 126 |

L | 133 |

LI | 140 |

LII | 143 |

LIII | 144 |

LIV | 147 |

LV | 148 |

LXV | 182 |

LXVI | 185 |

LXVII | 188 |

LXVIII | 189 |

LXIX | 191 |

LXXI | 195 |

LXXII | 199 |

LXXIII | 200 |

LXXIV | 205 |

LXXV | 208 |

LXXVI | 209 |

LXXVII | 214 |

LXXVIII | 221 |

LXXIX | 226 |

LXXX | 234 |

LXXXI | 242 |

LXXXII | 243 |

LXXXIII | 251 |

LXXXIV | 253 |

LXXXV | 255 |

LXXXVI | 257 |

LXXXVII | 258 |

LXXXVIII | 261 |

LXXXIX | 264 |

XC | 270 |

XCI | 271 |

XCII | 275 |

XCIV | 288 |

XCV | 294 |

XCVI | 305 |

XCVII | 310 |

XCVIII | 311 |

XCIX | 318 |

C | 322 |

CI | 329 |

CII | 334 |

CIII | 338 |

CV | 342 |

CVII | 346 |

359 | |

367 | |

### Common terms and phrases

acceleration angular arbitrary assume axes axis black hole calculate called clock components conservation Consider constant coordinate system coordinates course curve defined definition density depends derivative direction discussion distance effect Einstein element energy equal equation Exer expression fact field flat fluid flux force four frame function geodesic geometry given gives gravitational gravitational field horizon identical implies important independent indices integral light limit linear Lorentz manifold mass matrix means measured metric momentum moving Newtonian observer one-form orbit origin particle photon physical plane polar position possible proper Prove quantum mechanics radiation radius region relation relative rest result rotation Show solution space spacetime special relativity speed spherical star surface symmetric tensor theory transformation true unit universe velocity wave zero

### Popular passages

Page 359 - The theory of separability of the Hamilton-Jacobi equation and its applications to general relativity.