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| Hughston L.P., Tod K.P., Bruce J.W. — An Introduction to General Relativity |
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| Предметный указатель |
 2
Absolute derivative 71 78
Accelerated frames of reference 94
Adiabatic flow 42 44
Affine parametrization 73 f. 112 162
Age of one’s head, as compared with feet 111
Anisotropic cosmologies 170 f.
Arc length 15
Area distance 160—161
Area theorem 149
Bending of light 1 117
Bernoulli’s theorem 18
Bianchi classification of 3-dimensional Lie algebras 171 f.
Bianchi identity 59 88 90
Bianchi type I cosmologies, general solution for ideal fluids 179
Black hole explosions 149
Black holes 100 129 133—136 142
Blue shift (relativistic) 27
Boltzmann’s constant 41 91
Boyer — Lindquist coordinates for the Kerr solution 142—143
Cartan calculus 87 f.
Cartesian tensors 10 f.
Central pressure of star 141
Centre of mass, relativistic 44
Chandrasekhar, S. 135
Charge conservation 17
Charge, units for 18
Christoffel symbols 53 f. 90 101
Circular null geodesies 124
Classical tests of general relativity 117 f.
Closed time-like curves 145
Co-moving coordinates 155
Commutators of Lie derivatives 68
Commutators of skew products for symmetric tensors 70
Commutators of vector fields 10 68 79 107 108 170
Complex transformations 43
Compton scattering 30
Conformal invariance of null geodesies 74 131
Conformal Killing vectors 69
Conformal tensor (Weyl tensor) 95 100 141 169 181
Conformal transformations 65 75 131 136 169
Congruences of time-like geodesies 99 169
Connection 53 f. 93
Connection one-forms 87 f.
Constants of the motion 74 75 83 108 114—116 117 123 131
Continuity equation 40
Contravariant vectors 48
Coordinate patches 6 f. 46 57 126
Coordinate transition functions 46 f. 144
Cosmic censorship 135
Cosmological constant 168—169
Cosmological red shift 158 f.
Coulomb (unit of charge) 18
Covariant differentiation 6 53
Covariant vectors 49
Covariantly constant vectors 66
Critical density of universe 167
Current vector of a relativistic fluid 69 74
Curvature singularity 177
Curvature tensor 63 f.
de Donder gauge 103
De Motu, Newton’s remarks on the n-body problem 4
Death, by radial injection into a black hole 135
Deceleration parameter 167 f.
Deflection of light 1 117 121—122
Determinants 12—13 22
Differentiable manifold 6 46 48
Differential forms 86 f. 144
Differential geometry 2
Div, grad, curl, and all that 14
Divergence of a vector field 66 91
Dominant energy condition 100
Doppler effect 26 109 111
Duality 39 150
Dust 163 f. 176
d’Alembertian operator 103
Eddington — Finkelstein coordinates 127 f. 144
Eddington, A. 1
Einstein manifold 69
Einstein summation convention 10
Einstein tensor 9 64
Einstein — Cartan theory 56 94
Einstein, A. 2 f. 10 24 46 94 142 149 168
Einstein’s field equations 9 94 96
Electromagnetic field tensor 35 f.
Electromagnetic four-current 36 f.
Electrostatic unit (esu) 18
Ellipses, axes of 4 120 125
Energy conservation 26 f. 158
Energy density, electromagnetic 17
Energy density, fluid 9 40 74 91 157 163
Energy extraction from a black hole 147—149
Enthalpy, relativistic 42 44 68 75
Entropy, relativistic 41 f. 44 75 91
Epsilon identities 10 12 22 38—39 65—66
Equations of state 41 45 163
Equivalence principle 94 111
Ergosphere, of black hole 147—148
Eulers’s equation for ideal fluid, non-relativistic 9 18
Eulers’s equation for ideal fluid, relativistic 9 40 69
Event horizon 134—136 147 160
Exact solutions, Einstein’s remark on their difficulty 142
Extended Schwarzschild solution 126 f.
Exterior differentiation 52 88
Fine structure constant 17
First integrals 74 75 144—116
Focussing of geodesies 100 169
Foliations 19
Forms 85 f.
Four-momentum 26 f.
Friedmann equation 163
Friedmann — Robertson — Walker metric (FRW metric) 157 f. 163 174
Fundamental observers 155 169
Fundamental theorem of Riemannian geometry 8 67 94
Gauge transformations 16 103
Gauss theorem 16
Gauss, C.F. 2
Gaussian curvature 84
Generator of null cone 25
Geodesic deviation 76 f. 97 99 103
Geodesic equation 43 44 73—75 94—95 101 157 162
Geodesic field orthogonal to three Killing vectors 75
Geodesic hypothesis 73 93
Geometrical optics 162
Grassmann algebra 86
Gravitational collapse 133 f.
Gravitational constant 9 21 93—94 102 106—107 169
Gravitational waves 9 103
Habicht, C. 3
Hausdorff spaces 46
Hawking radiation 149
Helmholtz’s theorem, non-relativistic 20 23
Helmholtz’s theorem, relativistic 68—69
Herbert Spencer lecture, by Einstein 2
Hermitian matrices 22
Hilbert space 149
Homogeneity 151 f.
Homothetic Killing tensor 75
Hubble parameter 167 f.
Hubble, E. 2 168
Hubble’s law 171
Hydrostatic equilibrium 139 f. 142
Hypersurface orthogonality 90 107 175 179
Index free notation 85 f.
Index raising and lowering 25
Inertial trajectories 31
Initial value problem for Maxwell’s equations 23
Integral theorems of vector calculus 15
Interior solutions 137 f. 142
Invariant one-forms 173
| Inverse of matrix 13
Isentropic flow 44 68
Isotropic three-spaces 151 f. 155
Jacobi identity 70 170
Jacobian matrix for coordinate transition functions 49 f.
Kasner metric 175 f.
Kepler’s laws 4 124
Kerr solution 135 142
Kerr — Eddington coordinates 144
Kerr — Schild coordinates 145 f.
Kerr — Schild metrics 149—150
Killing tensors 43 69 83 150
Killing vectors 43 65 66 68 74 107—108 114 139 144—145 150 170
Kronecker delta 10 25
Lagrangians for geodesic equation 74 112 117
Lagrangians for Lorentz equation 116
Lagrangians for Newtonian orbits 123
Laplace’s equation 19
Le Verrier, U.J.J. 5 117
Leibniz property for covariant derivatives 55
Leibniz property for Lie derivatives 67
Leibniz property for skewed second covariant derivatives 61
Levi-Civita connection 8 60 63 69—70
Lie derivative 52 67 84 107
Lie groups 170 f.
Lie propagation 84
Light, time taken to travel around the universe 168
Light-cone 25 160 162
Linearized theory 103
Longitudinal and transverse components 31
Lorentz contraction 32 f.
Lorentz equation for charged particles, non-relativistic 17 23
Lorentz equation for charged particles, relativistic 40 45 99 116
Lorentz factor 26
Lorentz gauge condition 162
Lorentz transformations 32
Lorentzian metric 7 26 67
Luminosity distance 162
Magic density 167
Manifolds 46 f.
Mathematics, Einstein’s repect for 46
Matrices 12 f.
Maximally symmetric spaces 153
Maxwell, J.C. 35
Maxwell’s equations 16 f. 22 64 104
Metric connections 8 63 149
Metric tensor 7—8 25
Minkowski, H. 1 f. 24
Momentum, relativistic 26 f.
Multi-fluid cosmologies 169 179
Music, relation to creative process 3
n-sphere 48 91 153
n-torus 48
Navier Stokes equation 23
Newcomb, S. 117
Newton — Poisson equation 8 21 93 101 137
Newton, I. 4 5
Newtonian gravitation 4—5 20—21 92 98—99 101 116 117 124—125
Nonlinear character of Einstein’s theory 149
Normal vector to a surface 15
Null cones 1 25 160 162
Null geodesies 25 109 112 124 126 132 158 162
Null surfaces 131 147 150 159
Number density 41 91
Oblate ellipsoids 143
Oblate stars 116 124
Occam’s rasor, and torsion 94
Olympian Academy 3
Oppenheimer — Volkoff equation 139 f.
Orgies of formalism, Weyl’s remark 85
orthogonal matrices 22 170
Oxford University and a professor’s time machine 43
Oxford University and Einstein 2
p-forms 85 f.
Parallel propagation 81
Parallelepiped, volume of 12
Particle horizon 160
Particle interactions 27 f.
Pascal, B., on the universe as a hypersphere 151
Penrose, R. 147—149 181
Perihelion advance 3—6 117
Permutation tensor 10 12 22 38—39 65
Pfaffs theorem 50
Photon, emission and reception 27 109—111
Plancks’s constant 17 31 111
Plato 3 5
Potential vorticity 75
Poynting vector (electromagnetic energy flux) 17 100
Pressure 9 41 18 100 137 163
Principal null directions of electromagnetic field 44—45
Principal null directions of gravitational field 146—147
Probabilistic interpretation of quantum mechanics 149
Projection operator 31
Projective space ( ) 48
Projectively flat manifold 61
Proper length 32
Proper time 31
Quantum gravity, Einstein’s thoughts 148—149
Rank of a tensor 50
Red shift 8 109 133 158
Rest mass 26 f.
Ricci identities 58 f.
Ricci rotation coefficients 87 f.
Ricci scalar 64 100
Ricci tensor 60 64 99
Riemann tensor 57 f. 84 89 99
Riemann, B. 2
Riemannian connection 8 60 63
Ring singularity of Kerr solution 143
Rotating star 108 111 142
Rotation of geodesies 100 169
Scalar fields 48
Scalar triple product 11
Schwarzschild radius 106 f.
Schwarzschild solution 104 f.
Schwarzschild solution, interior 137 f.
Self-gravitating fluids 20 137
Seneca, on instability 133
Shearing of geodesies 100 169
Singularities 133 f. 143 177
Slow motion approximation 101 f.
Smoothness 48
SO(N) 154 170
Solo vine, M. 3
Sommerfeld, A. 46
Space-time continuum 6 24
Spaces of constant curvature 151
Special relativity 24 f.
Specific volume 41 91
Spherical symmetry 88 f. 104 116 133—135 138 151
Steady flows 19
Stellar inequalities 140—141
Stokes theorem 16
Stress tensor for electromagnetism 23 39 43.
Stress tensor for ideal fluid 9 20 40 68 157
Stress tensor for self-gravitating fluid 20 f.
Stress tensor for viscous fluid 23
Summation convention 10
Sun, bending of light 122
Sun, gravitational red-shift 111
Sun, Schwarzschild radius 106—107
Symplectic structure, associated torsion 66
Tangent vectors, to curves 71
Temperature, of relativistic fluid 41 f. 91
Tensor calculus 6 f. 10 24 46 85
Thermal radiation 169
Thermodynamical fluid 41 45 92
Time delay 124
Time dilation 8 33 110 158
Time Machine 43
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