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Stephani H. — Relativity: an introduction to special and general relativity
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Название: Relativity: an introduction to special and general relativityАвтор: Stephani H. Аннотация: Thoroughly revised and updated, this textbook provides a pedagogical introduction to relativity. It is self-contained, but the reader is expected to have a basic knowledge of theoretical mechanics and electrodynamics. It covers the most important features of both special and general relativity, as well as touching on more difficult topics, such as the field of charged pole-dipole particles, the Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools (tensor calculus, Riemannian geometry) are provided, most of the derivations are given in full, and exercises are included where appropriate. Written as a textbook for undergraduate and introductory graduate courses, it will also be of use to researchers working in the field. The bibliography gives the original papers and directs the reader to useful monographs and review papers.
Язык: Рубрика: Физика /Гравитационное взаимодействие /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 3rd editionГод издания: 2004Количество страниц: 396Добавлена в каталог: 02.10.2005Операции: Положить на полку |
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80 174 42 44 119 ðp-waves 244 Abelian group 286 Aberration 36 Acceleration parameter 356 371 372 Actio = reactio 30 Affine parameter 107 Angular momentum, for static fields 230 Angular momentum, of a source 224 Antisymmetric tensors 44 Approximation schemes 226 Asymptotically flat fields 346 Axisymmetric static vacuum solutions 295 Axisymmetric stationary vacuum solutions 296 Bach brackets 45 Balance equations 168 Balance equations for momentum and angular momentum 234 Beginning of the universe 373 368 369 Bianchi identities 143 Bianchi type I universe 381 Bianchi types of a group 287 Birkhoff theorem 188 Bivectors, self-dual 65 Black holes 307 327 336 Black holes and thermodynamics 340 Bogoliubov transformation 335 Boyer — Lindquist coordinates 322 Canonical equations for charged point particles 72 Cauchy problem 249 253 Causality 21 Centre of mass 32 Chandrasekhar limit 311 Characteristic initial value problem 255 Chazy — Curson particle 299 Christoffel symbols 97 107 Christoffel symbols for a spherically symmetric metric 186 Christoffel symbols, transformation law 110 Cigar singularity 383 Closed systems 2 4 5 Closed universes 298 360 Closed universes and Maxwell's equations 361 Closed universes and thermodynamics 363 Codazzi equation 253 Collapsing star 315 Collision of particles 31 Commutators 285 Compton scattering 34 Conduction current 86 Conformal curvature tensor 142 Conformal structure of a Friedmann dust universe 349 Conformal structure of Euclidian 343 Conformal structure of infinity 341 Conformal structure of Minkowski space 344 Conformal structure of the Schwarzschild solution 347 Conservation laws 154 291 Conservation laws and Killing vectors 288 Constraints 254 Contravariant components 42 117 Convection current 86 Coordinate transformations 109 Coordinates, canonical 140 Coordinates, comoving 111 262 Coordinates, Gaussian 111 Coordinates, locally fiat 113 Coordinates, locally geodesic 113 Coordinates, orthogonal 96 111 Coordinates, time-orthogonal 111 Coordinates, Weyl 295 Coriolis force 159 Cosmic background radiation 375 Cosmological constant 174 Cosmological models 380 Cosmological principle 352 Covariant components 42 117 Covariant derivative 127 Critical mass 314 Critical mass density 372 Critical mass of a star 311 Current four-vector 51 Curvature scalar 142 Curvature tensor 102 136 Curvature tensor and global parallelism 137 Curvature tensor and Killing vectors 281 Curvature tensor and second derivatives of the metric 139 Curvature tensor of a plane wave 242 Curvature tensor, reduction formulae 252 Curvature tensor, symmetries of 141 Curvature, extrinsic and intrinsic 251 Cylindrically symmetric solutions 297 de Sitter universes 148 365 Decay of particles 31 Deflection of light 194 Degenerate vacuum solutions 293 Differential operators 149 Doppler effect 35 Dragging of light 41 Duality rotation 58 Dualization of an antisymmetric tensor 48 121 Dust 90 176 Eddington — Finkelstein metric 305 321 Eigenvectors of 47 Eigenvectors of 46 Eigenvectors of antisymmetric tensors 47 Eigenvectors of Lorentz transformations 14 Eigenvectors of symmetric tensors 46 Eikonal 165 Einstein field equations 173 Einstein Ring 206 208 Einstein tensor 174 Einstein Universe 365 Einstein — Rosen waves 298 End of the universe 359 Energy balance for a particle in Special Relativity 27 Energy of the gravitational field 237 292 Energy-momentum Four-vector 28 Energy-momentum pseudotensor 230 Energy-momentum pseudotensor and balance equations 234 Energy-momentum pseudotensor of a plane wave 243 Energy-momentum tensor and thermodynamics 169 Energy-momentum tensor and variational principle 184 Energy-momentum tensor of a pure radiation field 68 Energy-momentum tensor of dust 90 170 Energy-momentum tensor of incoherent radiation 171 Energy-momentum tensor of perfect fluids 90 170 Energy-momentum tensor of the Maxwell field 55 87 163 entropy 169 Equations of motion and geodesic equation 99 Equations of motion for a spinning particle 180 Equations of motion for perfect fluids 171 Equations of motion in a Riemannian space 158 Equations of motion in Classical Mechanics 1 2 95 Equations of motion in Special Relativity 26 Equations of motion of test particles 178 Equations of motion with self-force 77 Equations of motion, charged point particles 69 72 Ergosphere of the Kerr solution 324 Euler's equation 89 Event horizon 325 360 370 Event horizon, surface area 328 Exact solutions 293 Expansion of a timelike vector field 265 Expansion of light rays 271 Extrinsic curvature 250 Far fields in the general case 227 Far fields, linearized theory 221 Far fields, time-independent case 230 Fermat principle 197 Fermi — Walker transport 132 161 Field equations 173 Field equations, linearized 219 Field equations, Newtonian limit 176 Field tensor of the Maxwell field 53 Fizeau experiment 41 Four-acceleration 25 Four-potential 52 Four-vectors 15 42 Four-vectors, normal forms 16 Four-velocity 25 158 Frequency shift in a gravitational field 354 Friedmann equation 364 Friedmann universes 367 383 Galilei transformations 5 Galilei's principle of relativity 5 Gauss equation 252 Gauss law 154 Gaussian coordinates 111 Gaussian curvature 144 Geodesic deviation 100 Geodesic equation 98 Geodesic null congruences 268 Geodesic precession 204 Geometrical objects 118 Geometrical optics 165 Goedel universe 384 Goldberg — Sachs theorem 277 Gowdy universes 298 Gravitational collapse 310 325 Gravitational collapse of spherically symmetric dust 315 Gravitational constant 174 Gravitational lensing 205 Gravitational radius 190 Gravitational waves 238 Gravitational waves in the linearized theory 240 Gravitational waves, exact plane 243 Gravitational waves, experimental evidence 248 Green's function of the wave equation 83 Groups of motion 283 Harmonic coordinates 219 Hawking effect 340 Homogeneity of space 2 Homogeneity of time 2 5 Hubble parameter 356 371 372 Hyperbolic motion 28 Incoherent matter 90 Incoherent radiation fields 171 Inertial system 1 Inflationary universe 374 Initial value problem 253 Initial value problem, characteristic 255 Integral laws 153 Integrals 150 Interior Schwarzschild solution 209 211 Intrinsic angular-momentum vector 181 Intrinsic curvature 251 Invariance, under Galilei transformations 4 Invariance, under rotations 3 Invariance, under translations 2 Invariants of a symmetric tensor 47 Invariants of an antisymmetric tensor 48 Invariants of the Maxwell field 165 Jacobi — Lie identity 285 Kasner metric 384 Kerr solution in Boyer — Lindquist coordinates 322 Kerr solution in Kerr coordinates 323 Kerr solution in Weyl coordinates 297 Killing tensors 289 Killing vectors 278 Killing vectors and conservation laws 288 Killing vectors and curvature tensor 281 Killing vectors of a sphere 281 Killing vectors of Minkowski space 280 Kruskal diagram of a collapsing star 320 Kruskal diagram of the Schwarzschild solution 306 Lemaitre metric 304 Length contraction 19 Lense — Thirring effect 225 Lie derivative 133 Lie groups 283 Lienard — Wiechert potentials 74 Light cone 16 Light deflection by the Sun 202 Light rays in the Schwarzschild metric 194 Light travel time 197 203 Limiting surface of stationarity 324 Line element, spherically symmetric 186 Linearized field equations 219 Linearized field equations and Maxwell equations 220 Linearized theory 217 Linearized theory, far fields 221 Local Minkowski system 112 Locally geodesic system 113 Lorentz force 51 55 56 Lorentz transformations 8 41 Lorentz transformations and null vectors 64 Lorentz transformations and pseudorotations 9 Lorentz transformations with arbitrarily directed velocity 12 Lorentz transformations, eigenvectors 14 Lorentz transformations, group property 10 Lorentz transformations, normal form 11 Lorentz transformations, orthochroneous 11 Lorentz transformations, proper 11 Lorentz — Abraham — Dirac equation 78 Lorentzian metric 106 Luminosity distance 356 Mass function 210 Mass, inertial and gravitational 104 Mass, velocity-dependence 26 Matching conditions for the gravitational field 257 Matching conditions for the interior Schwarzschild solution 212 Matching conditions for the Maxwell field 87 Maxwell equations and linear Einstein equations 220 Maxwell equations in a Riemannian space 162 Maxwell equations in closed universes 361 Maxwell equations in media 84 Maxwell equations in vacuo 50 52 Maxwell equations, conformal invariance 164 Maxwell fields and Lorentz transformations 61 Maxwell fields, algebraic classification 66 Maxwell fields, invariants of 165 Maxwell fields, non-degenerate 66 Maxwell fields, null 67 165 Maxwell fields, null eigenvectors of 67 McVittie solution 299 Mechanics in General Relativity 158 Mechanics in Special Relativity 24 Metric tensor 96 106 Michelson experiment 7 Minkowski coordinates 15 Minkowski space 14 Minkowski space, Killing vectors of 280 Monopole particle 80 178 Neutron star 311 Newman — Penrose tetrads 63 124 Newtonian limit 170 Normal-hyperbolic Riemannian space 112 Null fields, electromagnetic 67 165 Null geodesics 107 166 Null rotations 64 Null tetrads 63 124 Null vectors 16 63 268 Null vectors and Lorentz transformations 64 Null vectors, covariantly constant 244 Observables 291 Ohm's law 86 Optical scalars 269 Orthogonal transformations 3 Pancake singularity 384 Parallel displacement and covariant derivative 130
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