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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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Paradox 21 23 26 Paradox, pole-in-barn 26 34 Paradox, twin 23 26 28 Parallel-transport 163 165 168 171 175 Parallel-transport on a sphere 164 271 Parallel-transport, definition of 166 Parallel-transport, preserving scalar product 177 Parallelism as axiom in geometry 125 147 Parallelism on a sphere 164 Parallelism, global 165 170 177 Parallelism, local 165 PARAMETER 129 Parameter, affine 167 175 177 178 186 Parsec 318 Parsec, definition of 339 Past, absolute 15 Path 128 129 Penrose process 305 316 Perfect fluid 255 326 Perfect fluid, definition of 106 Perfect fluid, stress-energy tensor 107 115 Periastron, shift of 284 Perihelion 281 282 Perihelion, precession of Mercury's 198 282 Perihelion, shift of 280 283 310 312 313 Period of orbit in Schwarzchild metric 280 Perpetual motion 119 120 148 Phase space 80 176 Pion 33 Planck length 210 Planck mass 210 309 337 Planck temperature 341 Planck time 210 Planck's constant 52 266 309 Polar coordinates 130 Polar coordinates, bases 130 135 Polar coordinates, divergence in 138 Polar coordinates, Laplacian in 138 Polar coordinates, tensor calculus in 133 Polar coordinates, tensors in 126 Polar coordinates, unit basis 144 146 Polarization 238 244 248 Polarization, circular 231 245 Polarization, elliptical 245 249 Polarization, linear 219 220 230 245 249 Polarization, orthogonality 245 Polytrope 262 272 Pound — Rebka — Snider experiment 120 121 123 Precession, of Mercury's perihelion 282 Pressure 89 90 94 100 107 110 265 Pressure, gradient of 110 111 256 259 260 261 Pressure, quantum mechanical 266 267 Principle of equivalence see "Equivalence principle" Projection operator 87 248 Proper distance 218 322 330 341 Proper length 22 223 Proper length as affine parameter 167 178 Proper length of a curve 157 Proper radial distance 254 Proper surface element 163 Proper time 19 56 244 280 288 312 315 328 Proper volume 157 158 162 175 180 259 Proper volume of a sphere 180 Proper volume of a three-sphere 180 Proton 106 Pseudo-Riemannian space 80 PSR 1913+16 see "Binary pulsar system" Pulsar 266 271 274 288 Quadrupole moment tensor of binary star system 231 Quadrupole moment tensor of harmonic oscillator 230 Quadrupole moment tensor of various systems 247 Quadrupole moment tensor, definition of 229 Quadrupole moment tensor, trace-free 229 Quantum gravity 309 310 329 334 337 341 quantum mechanics 297 Quark 337 Quasar 241 288 311 319 Redshift 272 284 315 331 334 340 Redshift, central 274 Redshift, cosmological 330 Redshift, gravitational 119 123 255 Redshift, transverse Doppler 57 284 Relativistic gas 111 268 Relativity, principle of 2 13 21 23 Rest density 94 Rest mass 57 94 190 Rest mass, definition of 45 Rest mass, density of 100 Rest mass, energy associated with 46 Retardation 233 Ricci scalar 175 Ricci scalar in cosmology 323 Ricci scalar, definition of 174 Ricci tensor 175 196 Ricci tensor, definition of 173 Ricci tensor, symmetry of 173 178 Riemann tensor 147 175 Riemann tensor as commutator of covariant derivatives 171 Riemann tensor at Schwarzschild horizon 290 Riemann tensor for exact plane wave 220 Riemann tensor of flat space 170 Riemann tensor of Schwarzschild metric 315 Riemann tensor of weak field 203 Riemann tensor, components in locally flat coordinates 170 Riemann tensor, definition of 169 Riemann tensor, efficient ways to calculate 270 Riemann tensor, independent components of 170 178 Riemann tensor, independent of gauge 203 Riemann tensor, symmetries of 170 Riemannian space 80 141 177 Rindler space 150 Robertson — Walker metric 192 322 Robertson — Walker metric, closed 325 Robertson — Walker metric, definition of 324 Robertson — Walker metric, dynamics of 326 Robertson — Walker metric, Einstein tensor 339 Robertson — Walker metric, flat 325 Robertson — Walker metric, hyperbolic 325 Robertson — Walker metric, open 325 Robertson — Walker metric, spherical 325 Rotation 114 Rotation of black hole 303 Rotation, cause of Lense — Thirring effect 298 Rotation, effect on metric 213 Rotation, slow 265 Rotation, spatial 25 scalar 48 Scalar product 49 60 63 66 343 Scalar product, definition of 48 Scalar, field 153 Schwarzchild coordinates, inside horizon 290 Schwarzchild coordinates, singularity of at horizon 291 Schwarzchild coordinates, spacetime diagram 291 Schwarzschild interior solution 261 Schwarzschild solution 192 257 260 275 285 296 297 306 310 312 314 Schwarzschild solution in Kruskal — Szekeres coordinates 293 Schwarzschild solution, Christoffel symbols 315 Schwarzschild solution, coordinates inside horizon 290 Schwarzschild solution, orbit of photon in 304 Schwarzschild solution, orbits in 277 311 Schwarzschild solution, Riemann tensor 315 Schwarzschild solution, time dilation in 312 Separation vector 218 Simultaneity 18 23 118 320 322 Simultaneity, failure of 9 23 Singularity in cosmology 338 Singularity of Schwarzschild metric 315 Singularity, at center of star 273 Singularity, coordinate 288 291 310 Singularity, curvature 290 Singularity, theorems for cosmology 328 Singularity, true 293 310 Sources of gravitational waves, angular momentum loss 250 Sources of gravitational waves, binary star system 231 Sources of gravitational waves, collapsing mass 232 Sources of gravitational waves, harmonic oscillator 229 Sources of gravitational waves, luminosity of 240 Sources of gravitational waves, pair of oscillators 249 Sources of gravitational waves, slow-motion approximation 226 229 Space telescope 332 333 Spacetime diagram 6 Special relativity (SR) 1 3 4 6 15 21 26 27 46 49 53 61 74 80 89 93 110 118 119 123 150 154 155 161 184 185 188 198 202 204 Speed of light, and zero rest mass particles 53 Speed of light, universality of 2 3 10 12 24 26 Speed of sound 261 262 Sphere, intrinsic geometry of 164 Sphere, metric of 297 338 Spherical coordinates, singularity of 288 Spherical coordinates, volume element of 158 Spherical symmetry 276 323 Spherical symmetry in GR 251 Spherical symmetry, general metric for 253 Spherical symmetry, no gravitational waves in 233 249 258 Spinor space 80 SR see "Special relativity" Stability, of circular orbit 278 Static and spherical system, general metric of 254 Static limit see "Ergosphere" Static system, definition of 253 Stationarity 296 300 301 Stationarity and energy conservation 190 Stefan — Boltzmann constant 317 Stellar evolution 264 Stellar structure, Newtonian 260 269 Stellar structure, numerical calculation of 273 274 Stellar structure, relativistic 258 270 271 Stress 102 104 Stress-energy tensor 115 193 196 334 Stress-energy tensor for gravitational waves 249 Stress-energy tensor for static and spherical fluid 255 Stress-energy tensor of a perfect fluid 107 Stress-energy tensor of collisionless gas 115 Stress-energy tensor of dust 98 Stress-energy tensor of radiation 115 Stress-energy tensor, components in MCRF 101 Stress-energy tensor, definition of 98 Stress-energy tensor, examples of 114 Stress-energy tensor, Isaacson 249 Stress-energy tensor, symmetry of 99 103 Summation convention 37 40 55 Supergravity 310 Supernova 226 265 266 332 333 Surface element 96 Symmetry, axial 301 Symmetry, of Schwarzschild metric 315 Symmetry, reflection 301 Symmetry, spherical 233 Tangent vector 130 148 Tangent vector of a geodesic 175 Tangent vector, definition of 129 Tangent vector, parallel-transport of 166 Temperature 89 90 94 100 101 Temperature of a black hole 308 309 Tensor 60 Tensor operations 153 Tensor, antisymmetric 72 84 85 86 Tensor, antisymmetric part of 72 86 Tensor, basis 71 Tensor, Cartesian 81 Tensor, component transformation 78 87 Tensor, components of 62 Tensor, contravariant 78 Tensor, covariant 78 Tensor, definition of 61 77 Tensor, field 153 Tensor, metric 49 60 61 see Tensor, symmetric 72 84 85 Tensor, symmetric part of 72 68 Thermodynamics, first law of 100 106 Thermodynamics, of black holes 309 310 Thermodynamics, second law of 101 Three-sphere 179 Three-vector 39 Tidal force 125 173 232 315 316 Tidal force and geodesic deviation 173 Tidal radius 316 Time dilation 1 18 20 23 25 26 33 57 Time reversal invariance 253 Topographical map 68 Trace reverse operation 204 211 Transformation inverse 42 44 Transformation of basis one-forms 66 Transformation of basis vectors 40 Transformation of one-form components 63 Transformation of tensor components 78 Transformation of vector components 39 Transformation, matrix of 128 Transformation, singular 127 Turning point 278 302 313 327 Uncertainty principle 306 Units, geometrized 198 210 317 Units, natural 5 31 Units, SI 5 30 31 210 316 Universe, age of 308 Universe, closed 325 330 337 Universe, closure density 330 338 Universe, density of 329 334 338 Universe, expansion of 319 322 325 329 332 Universe, flat 325 Universe, global structure of 330 Universe, homogeneity of 321 322 Universe, hyperbolic 325 Universe, inflationary 337 Universe, isotropy of 321 322 Universe, matter-dominated 326 327 Universe, open 325 330 336 337 Universe, radiation-dominated 326 328 341 Universe, spherical 325 Universe, very early 308 Vacuum fluctuations 306—308 Vector 64 73 77 78 152 153 Vector as a function of one-forms 96 128 Vector as a tangent vector 130 Vector space, definition of 342 Vector space, dimension 342 Vector space, dual 63 64 75 76 85 Vector space, nonmetric 79 Vector, basis 39 40 54 62—65 80 83 88 133 Vector, basis in polar coordinates 130 Vector, components of 36 Vector, connecting 172 245 Vector, definition of 36 39 Vector, displacement 36 Vector, dual 64 Vector, gradient 69 74 132 Vector, magnitude 47 Vector, mapped to one-form 73 84 Vector, normal see "Normal" Vector, null 48 58 Vector, null basis 88 Vector, scalar product see "Scalar product" Vector, separation 218 Vector, spacelike 48 58 Vector, timelike 48 56 58 Vector, zero 48 54 Vectors, linear independence of 54 82 Velocities, Einstein composition of 25 33 56 Velocities, Galilean addition of 2 3 25 26 Velocity parameter 34 35 Velocity, absolute 2
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