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Schutz B.F. — A first course in general relativity
Schutz B.F. — A first course in general relativity

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Название: A first course in general relativity

Автор: 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: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 376

Добавлена в каталог: 29.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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      298 317
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
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