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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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Accelerated observer, in SR 150 Acceleration 44 51 244 278 Acceleration, absolute 3 Acceleration, uniform 56 150 Active galactic nuclei 310 311 Adiabatic 109 Angular diameter distance 341 Angular diameter, in cosmology 333 Angular momentum as source of metric 213 Angular momentum in collapse 296 Angular momentum in gravitational waves 250 Angular momentum in Kerr metric orbit 301 302 Angular momentum of a black hole 305 Angular momentum of star 265 Angular momentum of the Sun 274 Angular momentum, conservation of 191 Angular momentum, total 193 Angular velocity 280 Angular velocity of inertial frames 301 Angular velocity of zero-angular-momentum particle 298 Anisotropy 320 Anisotropy, dipole 335 336 Anisotropy, quadrupole 336 Aphelion 282 Area theorem see "Hawking's area theorem" Assumption of mediocrity 322 Asymptotic flatness 254 Baryon 106 Basis, non-coordinate 144 146 147 Basis, orthonormal 144 147 315 Basis, transformation of 40 Bianchi identities 173 175 200 257 Bianchi identities, contracted 174 Bianchi identities, twice-contracted 174 big bang 326 327 328 337 338 340 Binary pulsar system 284 314 Binary pulsar system as source of gravitational waves 232 241 Binary star system 265 Binary star system, gravitational wave effects on 250 Binary star system, orbit of 249 Birkhoff's theorem 258 Black body 339 Black body, luminosity of 317 Black hole 106 212 226 241 253 254 260 264 266 271 288 294 315 318 Black hole as a black body 308 309 Black hole collision 311 Black hole in modern astrophysics 310 Black hole, angular momentum of 305 Black hole, entropy of 310 Black hole, formed by collapse 295 Black hole, Kerr see "Kerr solution" Black hole, lifetime of 308 Black hole, luminosity of 308 Black hole, rotational energy of 305 Black hole, Schwarzschild see "Schwarzschild solution" Black hole, small 308 Black hole, stationary 296 Black hole, temperature of 308 Black hole, thermodynamics of 310 Black hole, tidal disruption by 316 Boltzmann's constant 274 308 Boyer — Lindquist coordinates, for Kerr metric 297 Buchdahl interior solution 262 273 Buchdahl's theorem 264 Calibration of axes 15 Cartan method 270 Cartesian coordinates 74 85 133 Causality 262 263 264 Center of momentum frame (CM) 47 Chandrasekhar limit 269 Christoffel symbols 135—137 161 162 166 169 172 180 185 188 191 Christoffel symbols and metric 140 142 150 Christoffel symbols for exact plane wave 220 Christoffel symbols for non-coordinate basis 146 150 Christoffel symbols for Schwarzschild metric 315 Christoffel symbols for weak gravity 187 Christoffel symbols, symmetry of 161 Christoffel symbols, tensorial nature of 143 Collapse 111 258 261 264. 294 Collapse as source of gravitational waves 232 Collapse to a black hole 295 Comma-goes-to semicolon rule 184 Comoving coordinates 322 323 Components, of a one-form 63 Components, of a tensor 62 71 77 78 Components, of a vector 36 Components, of the metric 60 62 Compton scattering 58 connecting vector 172 245 Conservation laws 47 Conservation, and symmetries of metric 189 194 275 Conservation, of angular momentum 191 Conservation, of charge 116 Conservation, of energy 105 109 112 190 196 197 306 Conservation, of energy-momentum 104 185 189 196 197 Conservation, of entropy 109 185 Conservation, of particles 106 184 Constraint equations 211 Continuum 89 Continuum approximation 90 113 114 Continuum, rigidity of 90 102 Contraction 63 68 137 153 173 175 Contravariant vector see "Vector" Conventions on indices 7 Conventions on Riemann tensor 169 Conventions on sign of interval 21 Coordinates, comoving 322 323 Coordinates, helpful 201 212 Coordinates, isotropic 272 Copernican viewpoint 320 Cosmic ray 58 Cosmological constant 199 212 327 329 Cosmological constant, cosmologies with 339 Cosmological principle 321 330 337 Cosmology 318 Cosmology, anisotropic 338 Cosmology, inhomogeneous 338 Cosmology, matter-dominated 326 Cosmology, radiation-dominated 326 Covariant derivative 136 137 153 160 175 Covariant derivative of a one-form 138 Covariant derivative of a scalar 137 Covariant derivative of a tensor 138 139 Covariant derivative of the metric 141 Covariant derivative, commutator of 170 Covariant derivative, commutes with index raising and lowering 174 Covariant derivative, definition of 161 Covariant derivative, product rule for 139 Covariant vector see "One-form" Covector see "One-form" Critical density 330 338 Curvature 160 163 Curvature and gravity 125 Curvature and tidal force 173 Curvature coordinates 252 Curvature coupling 184 Curvature of a sphere 164 Curvature, extrinsic 163 Curvature, intrinsic 163 167 Curve 129 166 Curve, definition of 128 Curvilinear coordinates 126 Cygnus X-1 266 312 Cylinder, intrinsic geometry of 166 D'Alembertian operator 205 Deceleration parameter 329 Decoupling 335 340 density 90 Density as a timelike flux 94 Density of electric charge 116 Density of electric current 116 Density of the Universe 319 329 334 Density, central 259 Density, cosmological perturbations of 335 336 Density, critical 330 338 Derivative of a determinant 162 Derivative of a function 67 80 Derivative of a one-form 138 Derivative of a scalar 137 Derivative of a tensor 80 138 Derivative of a vector 134 Derivative of basis vectors 133 Derivative, Lie 180 Derivative, Liebniz (product) rule for 86 Derivative, notation for partial 70 Derivative, partial 136 Detectors of gravitational waves 234 Detectors of gravitational waves, by light reflection 244 Detectors of gravitational waves, laser interferometers 222 Detectors of gravitational waves, quantum nondemolition 242 Detectors of gravitational waves, resonant oscillators 222 224 Detectors of gravitational waves, sources of noise in 225 Detectors of gravitational waves, space-based 222 Determinant 162 344 Differential geometry 73 Distance indicator 334 Distance scale, extragalactic 333 Divergence 137 177 Divergence in curved manifold 162 163 Divergence in polar coordinates 138 Doppler shift 53 Doppler shift, transverse 57 284 Dot product see "Scalar product" Dragging of inertial frames 298 301 Dust 107 Dust, definition of 90 Dust, stress-energy tensor for 97 98 Earth's motion in cosmology 335 Effective potential 277 305 Effective potential for cosmology 327 Effective potential for Kerr orbit 302 Einstein equations 197 199 200 208 215 220 256 328 337 Einstein equations for cosmology 326 Einstein equations for weak fields 204 205 Einstein equations for weak vacuum fields 214 Einstein summation convention 37 40 55 Einstein tensor 175 271 Einstein tensor for static and spherical metric 255 Einstein tensor in cosmology 326 339 Einstein tensor, definition of 174 Einstein tensor, efficient ways to calculate 270 Einstein, as celebrity 285 Electric charge of a black hole 296 Electric charge, conservation of 116 Electric charge, density of 116 Electric current four-vector 116 electric field 116 Electromagnetism see "Maxwell's equations" Element abundances, in cosmology 336 338 Element production 336 Element, of a continuum 89 Element, of a fluid 99 Element, of proper volume 158 162 175 Ellipse, polar equation of 283 Elsewhere, absolute 15 Energy at infinity 254 Energy of a particle 45 51 57 94 Energy of orbit in Schwarzschild metric 278 Energy, conservation of 105 109 112 190 196 197 Energy, density of 89 97 99 100 101 267 326 Energy, difficulty of defining 239 Energy, flux of 99 101 104 Energy, frame-invariant expression for 52 Energy, Galilean kinetic 46 Energy, in Kerr metric orbit 301 Energy, internal 100 Energy, negative 303 304 307 Energy, negative and Hawking process 306 Energy, positivity of 297 Energy, relative to ZAMO 304 Energy, total 188 Energy-momentum, conservation of 104 185 189 196 197 entropy 100 101 106 256 Entropy of a black hole 310 Entropy, conservation of 109 185 Equation of state 115 256 261 269 273 274 328 339 Equation of state for cold electron gas 268 Equation of state for photon gas 115 Equation of state, Buchdahl's 272 Equivalence principle 121 122 187 Equivalence principle, strong 122 184 185 196 Equivalence principle, weak 122 Ergoregion 299 304 317 Ergoregion and Penrose process 305 Ergoregion, unstable in a star 305 Ergosphere 300 Ergosphere of Kerr metric 299 Ergosphere, orbit in 317 Ergotoroid, in rotating star 299 Euclidean space 74 125 Euler's equation 192 Event 6 7 Expansion of the universe 319 322 325 329 Far field, of stationary body 206 Faraday tensor 117 Faraday tensor, antisymmetry of 116 Fermi gas 270 Fermi momentum 267 268 Flat space 125 160 Flat space, Riemann tensor of 170 Fluid 89 90 Fluid dynamics 184 Fluid element 99 Fluid element, four-velocity of 100 Flux 91 92 94 95 96 331 333 Flux of radiation 115 Flux, across surfaces of constant time 95 Flux, frame-dependence of 93 Force four-vector 114 Four-acceleration 51 57 109 Four-momentum 52 57 94 97 185 Four-momentum of photons 52 Four-momentum, conservation of 46 57 58 104 185 Four-momentum, definition of 45 Four-momentum, Galilean 113 Four-momentum, total 47 188 189 Four-vector 39 Four-velocity 46 50 51 56 57 67 86 100 Four-velocity, definition of 44 Four-velocity, non-existence of for photons 52 Frequency, of a wave 215 Function 61 62 Function, derivative of 67 Future, absolute 15 Galaxy cluster 319 Galaxy formation 334 Gas, electron 268 Gas, Fermi 270 Gas, photon 115 268 Gas, relativistic 111 268 Gauge invariance 211 Gauge theories 337 Gauge transformation 201 202 204 238 Gauge transformation, definition of 203 Gauge, de Donder 204 Gauge, harmonic 204 Gauge, Lorentz 204 205 211 216 229 Gauge, transverse-traceless (TT) 216 218 223 229 234 244 248 Gauss' law 105 111 112 114 117 157 162 163 209 227 228 296 General relativity (GR) 3 80 110 122 125 148 155 174 197 199 201 205 206 208 239 251 261 281
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