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Schutz B.F. — A first course in general relativity
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Название: A first course in general relativityАвтор: Schutz B.F. Аннотация: General 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.
Язык: Рубрика: Физика /Гравитационное взаимодействие /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1985Количество страниц: 376Добавлена в каталог: 29.09.2005Операции: Положить на полку |
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Предметный указатель
General relativity (GR), field equations see "Einstein equations" Geodesic 125 163 173 175 189 217 220 Geodesic as path of freely falling particle 125 183 Geodesic deviation 171 218 223 245 315 Geodesic deviation for weak field 193 Geodesic deviation, equation of 173 Geodesic, definition of 166 Geodesic, extremal length of 167 Geodesic, null 177 275 307 313 321 340 Geodesic, spacelike 177 Geodesic, timelike 177 183 275 Geodesic, uniqueness of 167 Geometrical object 36 93 GR see "General relativity" Gradient 66 70 Gradient as a one-form 68 Gradient of a tensor 81 Gradient, vector associated with 69 74 132 Grand unified theory 337 Gravitational field 3 4 Gravitational field of a rotating source 213 Gravitational field, far from relativistic source 206 Gravitational field, nonuniformities of 124 Gravitational field, tidal see "Tidal force" Gravitational field, weak 185 200 201 271 Gravitational potential energy 188 190 259 271 Gravitational waves 208 226 228 322 Gravitational waves, absence of in spherical symmetry 233 249 258 Gravitational waves, angular momentum flux 250 Gravitational waves, astrophysical interest in 221 Gravitational waves, detectors of 222 Gravitational waves, dispersion relation 215 Gravitational waves, driving harmonic oscillator 223 Gravitational waves, energy 234 Gravitational waves, energy flux 235 236 238 249 Gravitational waves, exact solution for plane wave 219 Gravitational waves, frequency 215 Gravitational waves, from collapse 296 Gravitational waves, generation of see "Sources of gravitational waves" Gravitational waves, in Kerr metric 310 Gravitational waves, ingoing and outgoing 227 Gravitational waves, plane 215 237 Gravitational waves, polarization 219 238 Gravitational waves, propagation of 214 Gravitational waves, quadrupole approximation 229 Gravitational waves, traveling at speed of light 215 Gravity, alternative theories 197 Gravity, as curvature 118 Gravity, special relativistic theory 120 Group theory, and symmetry 270 Group, Lorentz 87 88 Group, orthogonal 88 harmonic oscillator 222 223 235—237 248 249 Hawking process 305 309 310 Hawking's area theorem 296 300 316 Heat, conduction of 102 106 Hilbert space 75 Hilbert, also derived GR equations 197 Hipparcos satellite 285 287 333 Homogeneity 319 320 324 329 334 336 339 Homogeneity of early universe 328 Homogeneity of hyperbolic universe 326 Horizon 150 293 294 299 300 303 306—308 310—312 315 321 Horizon of Kerr metric 302 Horizon of Schwarzschild metric 289 290 291 295 Horizon, area of 300 Horizon, definition of 290 Horizon, particle 321 Horizon, proper time to reach 289 Horizon, stationary 296 Hubble flow 319 Hubble law 329 330 Hubble law, anisotropic version 339 Hubble's constant 320 330 333 340 Hydrostatic equilibrium, equation of 260 Hydrostatic equilibrium, in GR 192 256 Hyperbola see "Invariant hyperbola" Hyperplane 151 Hypersurface 47 111 193 320 322 325 329 Hypersurface, null 77 Hypersurface, spacelike 77 Hypersurface, timelike 77 Impact parameter 280 285 286 311 312 Index, barred 37 40 Index, contravariant 78 Index, covariant 78 Index, dummy 38 40 41 54 71 76 169 Index, free 38 54 256 Index, Greek 7 21 127 Index, Latin 7 21 38 Index, raising and lowering of 78 79 174 Inertial frame 5 118 326 Inertial frame, dragging of 298 301 Inertial frame, freely falling 122 123 187 Inertial frame, global 156 Inertial frame, globally incompatible with gravity 119 123 Inertial frame, local 123—125 155—157 169 183 184 190 290 307 Inertial frame, not at rest on Earth 120 Inertial mass, density of 110 Inertial observer 3—5 Inflationary universe 337 Inhomogeneity 319 338 Initial-value problem 200 Inner product see "Scalar product" Instability, of circular particle orbit 278 Instability, of circular photon orbit 278 Instability, of ergoregion of star 305 Instability, of white dwarf 269 270 Instability, rotational 317 Integrability conditions, for coordinate basis 147 Integrability conditions, for global parallelism 177 Interior solutions, Buchdahl 262 273 Interior solutions, exact 261 Interior solutions, Schwarzschild 261 272 Internal energy 100 Interval, invariance of 10 14 24 Interval, lightlike 14 Interval, null 14 Interval, spacelike 14 35 118 Interval, timelike 14 35 118 326 Intrinsic curvature 251 Intrinsic metric 300 Invariant hyperbola 15 326 339 Ionization of hydrogen, in cosmology 335 Isaacson stress-energy tensor 249 Isotherm 83 Isotropic coordinates 272 Isotropy 319 323 324 Isotropy of early universe 328 Isotropy of hyperbolic universe 326 Jacobian 126 127 148 157 Kerr solution 192 296—298 303 317 Kerr solution, area theorem for 316 Kerr solution, horizon of 302 Kerr solution, inverse metric 301 Kerr solution, orbit of photon 304 Kerr solution, Penrose process in 305 Kerr solution, photon orbits in 300 Kerr solution, symmetry of 310 Killing vectors and conserved quantities 194 Killing's equation 194 kinetic energy 190 Kronecker delta 11 43 49 79 344 Kruskal — Szekeres coordinates 316 Kruskal — Szekeres coordinates, definition of 292 Kruskal — Szekeres coordinates, spacetime diagram 293 Laplace's equation 208 Laplacian 137 Laplacian in polar coordinates 138 Lens, gravitational 285 287 Lense — Thirring effect 298 Lie bracket 180 Lie derivative 180 Light cone 14 15 233 292 Light cone for Kruskal — Szekeres coordinates 292 Light cone in cosmology 322 329 Light cone in Schwarzschild metric 291 Light deflection 285 310 Light deflection, by Jupiter 287 Light deflection, by the Sun 198 286 Light deflection, partial 287 313 Line element 192 331 Line element in Boyer — Lindquist coordinates 297 Line element in cosmology 323 Line element in Kruskal — Szekeres coordinates 292 Line element in null coordinates 220 Line element of Minkowski space 220 Line element of polar coordinates 132 Line element of spherically symmetric spacetime 253 Linear independence 342 Linearity 61 63 Linearized theory 205 219 310 322 Local flatness 315 324 Local-flatness theorem 156 159 163 176 Locally flat (inertial) coordinates 154 158 165 172 173 175 180 Lorentz contraction 1 18 20 25 26 33 91 Lorentz frame see "Inertial frame" Lorentz transformation 1 18 23 24 25 33 35 37 38 48 53 55 56 58 117 128 160 194 202 339 Lorentz transformation as a group 87 Lorentz transformation, background 201 202 216 238 245 luminosity 115 331 332 333 341 Luminosity distance 330 332 Luminosity in cosmology 333 Luminosity of a black hole 308 309 Luminosity of black body 317 Magnetic charge, of a black hole 296 Magnetic field 116 265 Magnitude 341 Main sequence 265 Manifold 151 176 Manifold, affine 154 Manifold, coordinates of 151 Manifold, differential structure of 152 Manifold, differentiate 152 182 Manifold, dimension of 151 Manifold, local flatness of 154 158 161 Manifold, metric of 154 Manifold, pseudo-Riemannian 154 Manifold, Riemannian 154 175 Mass function of spherical metric 257 Mass of a relativistic source 208 Mass of a star 259 265 Mass of the Sun, geometrized 199 Mass, density of 110 195 Mass, limit for neutron stars 266 270 274 Maxwell's equations 116 211 Maxwell's equations in curved spacetime 184 MCRF 44 45 47 49—51 53 56 90 94 96—103 106—109 114 115 124 184 195 Mercury, perihelion precession 198 282 Metric 49 60 69 71 154 176 see Metric as a mapping 73 78 Metric as a symmetric tensor 72 Metric of a weak gravitational field 185 Metric of Euclidean space 141 Metric of three-sphere 179 Metric, components of 60 62 Metric, components of in polar coordinates 131 Metric, covariantly constant 141 Metric, intrinsic 300 Metric, inverse 74 76 78 154 Metric, inverse in polar coordinates 132 Metric, physically measurable 118 119 182 Metric, positive-definite 288 Metric, Schwarzschild see "Schwarzschild solution" Metric, signature of 155 175 Metric, useful identities for 179 Michelson — Morley experiment 3 Microwave background radiation 58 221 335 336 338 Minkowski space 1 26 88 125 158 179 182 193 194 201 227 251 325 339 Minkowski space, background 204 216 Missing mass 338 Momentarily comoving reference frame see "MCRF" Momentum as a frame-dependent vector 113 Momentum of a particle 51 94 Momentum, conservation of 105 196 197 Momentum, density of 89 98 99 102 104 Momentum, Fermi 267 268 Momentum, flux of 99 102 107 Momentum, spatial 45 307 Momentum, total 188 Nearly-Lorentz coordinates 200 201 Neutron 106 Neutron star 111 212 261 266 269—271 314 318 Newtonian gravity 110 187 188 192 205 231 249 261 268 278 282 318 Newtonian gravity as a physical theory 183 Newtonian gravity, field equation for 206 Newtonian gravity, geodesic deviation in 193 Newtonian gravity, Riemann tensor for 193 Newtonian gravity, source of 195 Newtonian limit 199 205 208 212 264 272 Newtonian potential 185 199 226 232 241 Newtonian potential of a relativistic source 207 Norm 343 Normal, null 76 Normal, one-form 70 83 95 111 Normal, outward 70 77 85 111 Normal, unit 76 85 95 111 193 Normal, vector 70 76 Number, conservation of 106 184 Number, density of 92 94 100 118 Number, flux of 92 118 Number-flux vector 93 Number-flux vector for fluid 100 Observation, defined 4 Observation, visual 5 One-form 67 73 77 78 95 127 128 152 153 One-form, basis 64 65 80 82 83 One-form, basis in polar coordinates 130 One-form, basis transformation 65 One-form, Cartesian 74 One-form, component transformation 63 One-form, components of 63 One-form, definition of 62 One-form, magnitude 76 One-form, mapped to vector 73 84 One-form, null 76 One-form, picture of 66 68 One-form, spacelike 76 One-form, timelike 76 One-form, unit basis 131 One-form, zero 64 One-forms, linear independence of 65 82 One-forms, scalar product of 76 Oppenheimer — Volkov equation 258 262 Orbit in Kerr metric 302 304 Orbit in Newtonian gravity 281 282 Orbit in Schwarzschild metric 277 311 Orbit, angular velocity 280 Orbit, circular 278 280 317 Orbit, not closed in Schwarzschild metric 281 Orbit, period of 280 Orbit, photon 279 Orbit, plunge 279 Orbit, stable 278 Orbit, turning point 278 Orbit, unstable 278 Orthogonal matrix 85 88 Orthogonality 48 49 293 Orthonormality 48 315 343 Outer product 71
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