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Ludvigsen M. — General relativity. A geometric approach
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Название: General relativity. A geometric approachАвтор: Ludvigsen M. Аннотация: Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.
Язык: Рубрика: Физика /Гравитационное взаимодействие /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1999Количество страниц: 217Добавлена в каталог: 18.09.2005Операции: Положить на полку |
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Absolute time 3 Abstract index notation 56 Abstract indices 57 Affine space 28 62 Affine tangent vector 96 Angular momentum parameter 128 Angular momentum, intrinsic 77 132 Area function 136 Area theorem 159 170 Arrow of time 177 Asymptotic flatness 115 Asymptotic flatness, definition of 118 Background radiation 187 191 Beforeness 9 Bianchi identities 90 big bang 8 179 Big bang, singularity 185 Birkhoff’s theorem 134 139 Black hole 155 Black hole, entropy 170 Black hole, temperature 170 Black-hole region 158 Blackbody radiation 188 Blackbody signature 187 Blackbody spectrum 8 190 191 Boltzmann constant 188 Bondi coordinate system 121 Bondi factor 24 Bondi scaling 120 Cauchy hypersurface 150 Caustic point 158 Charge density 38 Chart 82 clock 10 Closed Universe 180 Comoving observer 7 177 Compatible symmetries 122 Compton scattering 43 Conformal completion 118 Conformal freedom 120 Conformal rescaling 110 Congruence 63 83 Congruence, parametrized 63 Connection 86 Conservation equation 70 Conserved current 77 Constant curvature 94 183 Continuity equation 70 Coordinate system 82 Cosmic censorship hypothesis 160 Cosmological constant 100 187 Cosmological principle 6 175 Cosmology 6 Covariant derivative 84 86 Covector 52 Critical density 180 Current density 37 Curvature tensor 5 89 96 137 Derivation 63 83 Directional derivative 61 Divergence 65 Divergence function 106 157 Doppler shift 25 Dust particles 103 Early Universe 7 Einstein equation 5 Einstein tensor 91 Einstein’s field equation 100 Elastic time 178 Electric charge 71 electromagnetic field 49 Energy of a gravitational field 131 Energy-momentum tensor 5 43 73 100 Entropy of photon gas 189 Entropy, per baryon 194 Entropy, specific 194 Equation of state 185 186 Equatorial Killing field 141 Ergosphere 167 Euclidean geometry 4 Euler equation 70 Event 3 12 Event, pointlike 12 Expansion factor 177 Four-acceleration 48 Four-momentum 41 Four-momentum density 43 Four-momentum of a photon 33 Four-velocity 28 Friedmann equation 183 Future null infinity 116 117 Gauss’s theorem 74 76 77 131 Generalized entropy 170 Generalized second law 171 Geodesic 96 Geodesic deviation 99 Geodesic equation 96 141 Global Cauchy hypersurface 157 Gradient 61 84 Gradient operator 86 Gravitational collapse 152 Gravitational constant 10 Gravitational entropy 177 Gravitational mass 138 140 Gravitational radiation 116 Gravitational red shift 125 143 handedness 9 Hawking effect 170 Homogeneity of the Universe 177 Hubble’s law 178 Identity tensor 53 Incomplete geodesic 156 Inertial observer 4 Inertial particle 13 96 Initial conditions 6 Intrinsic angular momentum for Kerr spacetime 163 Isotropic 6 Isotropy of the Universe 177 Kerr angular velocity 165 Kerr congruence 111 Kerr event horizon 164 Kerr mass 130 Kerr metric 130 Kerr spacetime 126 128 132 161 Killing equation 122 Killing field 77 Killing tensor 164 Killing vector 122 Killing vector, asymptotic normalization 126 Komar energy 132 Kronecker delta 36 Kruskal diagram 148 Kruskal spacetime 147 Laplace 152 Latitudinal angle 127 128 161 Leibniz condition 63 86 Levi-Cevita tensor 36 55 73 89 Lie bracket 64 88 Lie derivative 64 122 Lie propagation 66 Light-second 10 Longitudinal function 130 Lorenz transformation 36 Magnetic charge 71 Magnetic current 72 Magnetic part 59 Manifold 83 Mass parameter 128 Maxwell equations, vacuum 62 Maxwell field, Coulomb 62 Maxwell field, electric part 59 Maxwell tensor 49 54 Maxwell tensor, dual of 72 Maxwell’s equations 70 72 Metric connection 88 Metric, rescaled 118 Metric, signature 86 Naked singularities 160 Neutrino background 187 Neutron star 152 Newtonian gravity 101 Newton’s laws 100 No-hair theorem 160 Null cones 16 Null congruence, shear-free 110 Null congruence, surface-forming 106 Null fluid 101 Null function 97 Null generators 97 Null geodesies 85 97 Null tetrad 108 109 Open set 82 Open Universe 180 Orientation, spacelike 86 Orientation, temporal 86 Paracompactness 83 Parallel propagation 88 Parameter function 63 Particle horizon 181 Perfect cosmological principle 176 Perfect fluid 47 70 183 Perihelion 142 Perihelion, advance 145 photons 4 Planck’s constant 10 Planck’s law 33 Plane-wave 62 Point in space 3 Position vector 28 Position vector field 61 Pressure 48 70 Principal null directions 147 Principal null vectors 161 Principle of equivalence 81 Principle of relativity 4 14 Proper time 17 Quantum gravity 177 quantum mechanics 6 Radial function 116 Radiation-filled universe 186 Raychaudhuri equation 104 136 Raychaudhuri equation for a null congruence 108 Red shift, cosmological 178 Red-shift factor 125 Relativistic continuity equation 101 Relativistic Euler equation 101 Rest mass 41 Ricci curvature 119 120 Ricci tensor 91 Riemann zeta function 189 Scalar curvature 91 Scaling factor 177 183 Schwarzschild geometry 134 146 Schwarzschild horizon 147 Schwarzschild metric 140 Schwarzschild radius 152 Schwarzschild singularity 147 Schwarzschild spacetime 139 147 Schwarzschild throat 149 Shear of a null congruence 108 Shear of timelike congruence 104 Singular spacetime 156 Singularity theorems 8 155 Smooth space 82 Smooth structure 82 Smoothness 82 Spacetime 3 Spacetime geometry 4 Spacetime metric 4 30 Spacetime, algebraically special 111 Spacetime, axisymmetric 123 Spacetime, inextendible 85 156 Spacetime, metric 85 Spacetime, predictable 150 Spacetime, singularity 152 156 Spacetime, static 123 Spacetime, stationary 123 Spacetime, symmetry 115 122 Spherical symmetry 135 Spin 77 Standard model 6 Static universe 184 Stationary observer 125 126 Stefan — Boltzmann constant 188 Stefan — Boltzmann law 188 Streamlines 63 Strong energy condition 44 104 Summation convention 29 Surface gravity 166 Surface integral 77 Symmetry family 52 Tangent vector 84 Tensor 51 Tensor product 52 Tensor, anti-self-dual 73 Tensor, components 52 Tensor, contractions 53 Tensor, field 61 Tensor, self-dual 73 Tensor, simple 53 Tensor, trace 54 Thermal equilibrium 7 Thermodynamics of black holes 169 Thermodynamics, classical 170 Three-momentum 42 Tidal effects 81 96 Torsion-freeness 87 90 TP-symmetry 123 Trapped surface 149 157 158 Twist 111 universal time 177 Weak energy condition 43 47 Weyl tensor 92 White dwarf 152 World line 3 12 World tube 74 134
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