## 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 | 3 |

III | 6 |

IV | 7 |

V | 8 |

VI | 9 |

VII | 12 |

VIII | 17 |

IX | 20 |

LIX | 153 |

LX | 156 |

LXI | 162 |

LXII | 165 |

LXIII | 169 |

LXIV | 175 |

LXV | 177 |

LXVI | 178 |

X | 26 |

XI | 27 |

XII | 28 |

XIII | 29 |

XIV | 30 |

XV | 32 |

XVI | 38 |

XIX | 41 |

XX | 46 |

XXI | 47 |

XXII | 49 |

XXIII | 52 |

XXIV | 54 |

XXV | 55 |

XXVI | 56 |

XXVII | 62 |

XXX | 63 |

XXXI | 64 |

XXXII | 73 |

XXXIII | 75 |

XXXIV | 79 |

XXXV | 80 |

XXXVI | 82 |

XXXVII | 83 |

XXXVIII | 91 |

XL | 92 |

XLI | 96 |

XLII | 99 |

XLIII | 101 |

XLIV | 108 |

XLV | 112 |

XLVI | 113 |

XLVII | 114 |

XLVIII | 115 |

XLIX | 120 |

LI | 128 |

LII | 135 |

LIII | 142 |

LIV | 145 |

LV | 146 |

LVI | 149 |

LVII | 150 |

LXVIII | 184 |

LXX | 187 |

LXXI | 190 |

LXXII | 191 |

LXXIII | 193 |

LXXIV | 197 |

LXXVI | 201 |

LXXVII | 202 |

LXXVIII | 207 |

LXXIX | 210 |

LXXX | 211 |

LXXXI | 216 |

LXXXIII | 223 |

LXXXIV | 228 |

LXXXV | 236 |

LXXXVI | 244 |

LXXXVII | 245 |

LXXXVIII | 253 |

LXXXIX | 255 |

XC | 257 |

XCI | 259 |

XCII | 260 |

XCIII | 263 |

XCIV | 266 |

XCV | 272 |

XCVI | 273 |

XCVII | 277 |

XCVIII | 290 |

XCIX | 296 |

C | 307 |

CI | 312 |

CII | 313 |

CIII | 320 |

CV | 324 |

CVI | 331 |

CVII | 336 |

CVIII | 340 |

CX | 344 |

CXI | 348 |

361 | |

369 | |

### Common terms and phrases

acceleration algebra angular momentum arbitrary axis basis vectors black hole calculate called Christoffel symbols clock components conservation const constant coordinate system covariant derivative curvature curve defined definition Derive Eq differential discussion distance Einstein energy Euclidean space Exer flat fluid element flux four-momentum four-velocity freely falling function galaxies gauge geodesic geometry gives gradient gravitational field gravitational waves horizon hyperbolae independent inertial frame integral line element linear Lorentz transformation manifold matrix MCRF measured metric tensor Newtonian notation null number density observer one-form orbit orthogonal oscillator parameter particle photon physical plane polar coordinates radiation radius real number redshift relative relativistic rest mass Riemann tensor rotation scalar Schwarzschild Schwarzschild metric Show solution spacetime diagram spatial sphere star stress–energy tensor surface tangent theory timelike trajectory vanish velocity world line zero

### Popular passages

Page 361 - The theory of separability of the Hamilton-Jacobi equation and its applications to general relativity.