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| Ïîèñê ïî óêàçàòåëÿì |
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| Foster J., Nightingale J. — A Short Course in General Relativity (Longman mathematical texts) |
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| Ïðåäìåòíûé óêàçàòåëü |
 ( ) 86
 symbol 6
 (the field of real numbers) 2 6
Absolute derivative 39 41
Acceleration in rotating frame 66
Addition of velocities 168—169
Affine connection 40
Affine parameter 49
Age of universe 157—158
Arc length 37 49
Background radiation 149
Basis vectors 3—12 21 22 34
Basis, change of 3 4 8 14 21 22
Basis, natural 34
Bending of light xv 117—120
Bianchi identity 78
Black holes 93 113 123—127
Blueshift 102—105
Boosts 166—167 179
Cartesian coordinate system 54
Cartesian product 9
Centrifugal force 66
Charge density 181 182
Chart 29 93
Christoffel symbols, first and second kind 46—47
Coderivative see "Covariant derivative"
Components of a tensor 12—16 37
Components of a vector 3 8
Compton effect 111
Connection coefficients 39 40 45—46
Conservation of energy-momentum 177
Continuity equation 73 74 152
Continuum, 4-dimensional spacetime 163
Contraction of tensors 15
Contraction, Lorentz 170—171
Contravariant tensors (tensors of type (r, 0)) 12
Contravariant vectors 7 36
Coordinate systems 27—28 54 60 128 150
Coordinate, curve 34
Coordinate, neighbourhoods 29 31—33
Coordinate, ranges 93
Coordinate, velocity (of light) 98 114
Coordinate, velocity (of particles) 72 109—110 175
Coriolis force 66 67
Cosmological constant 158
Cosmological principle 150
Cosmology 148—162
Covariance, principle of general xv
Covariant derivative 44 76
Covariant tensors (tensors of type (0, s)) 12
Covariant vectors 7 36
Curl 69
Current 4-vector 182
Curvature 25—28
Curvature scalar 79
Curvature tensor, Riemann — Christoffel 76—77
Cyclic identity 77
d'Alembertian 135 182
Deceleration parameter 154 156 162
Deflection of light xv 117—120
Density, charge 181 182
Density, critical 154 156
Density, mass 72 183
Derivatives, absolute 39—43
Derivatives, covariant 44 76
Distance in Schwarzschild field 96—97
Divergence 47 76
Doppler effect 178—180
Doppler effect, transverse 180
Dual spaces 6—8
Dummy suffices 4
Eddington — Finkelstein coordinates 124
Einstein cosmological model 157—158
Einstein summation convention 2
Einstein tensor 79
Electromagnetic field tensor 182 184
Electromagnetic potential 182
Elevator, freely falling xii
Energy and mass 175 176
Energy-momentum 4-vector 72 175
Equations of motion of fluid 73—76 152
Equations of motion of particle in gravitational field 105—112
Equivalence of Euler — Lagrange and geodesic equations 51
Equivalence principle xi—xiii
Euler equation for fluid 75
Euler — Lagrange equations 50 69 106
Event 54 163
Expansion of universe 158
Falling particle 107—110
Field equations, Einstein 82—85 151
Flatness 25—28 77
Fluids 72—76 148
Force, Lorentz 183
Four-force 57 176
Four-vectors 71—72 174—176 182
Friedmann equation 152
Friedmann models 153—157
Functionals, bilinear 9
Functionals, linear 6
Functionals, trilinear 11
Functions, vector space of 6
Fundamental theorem of Riemannian geometry 46
Galilean transformation 168 183
Galileo xii
Gauge condition, Lorentz 135 181
Gauge transformations 134 181
Gauge TT 138
Geodesic 48—49
Geodesic and Newton's laws 59
Geodesic coordinates 48
Geodesic deviation 26 79—81
Geodesic deviation (Newtonian) 84
Geodesic effect xvi 120—123
Geodesic postulate 57
Geodesic, equation of 49 57 80
Gradient 36
Gravitational mass xi
Gravitational radiation 132—147
Gravitational redshift 100—105
Gravitons 147
Gyroscope experiment 120—123
Homogeneity of space 148 150
Horizon, event 126—127
Horizon, particle 162
Hubble's constant 149 156 162
Hubble's Law 149 154 157 158
Hydrodynamical equations 75—76
Hypotheses of general relativity xiii xv 57
Hypotheses of special relativity 163—164
Impossibility of transforming away gravity xiii 129
Inertia tensor 21
Inertial frame of reference 54 55 163
Inertial mass xi
Inner product 17—19 165
interval 37 164—165
Invariant quantities 164 165
Isomorphism, natural 8
Isotropic coordinates 91 128
Isotropy of space 149 150
Kepler's third law 110
Kronecker delta 4 16 19
Kruskal coordinates 129
Lagrange's equations 50 69 106
Lagrangian 50
Length in special-relativity 170—171
| Length near star 94—97
Length of a curve 37
Length of a vector 19
Light cone 125 172—173
Light ray, path of 113—114 117—120
Line element 37 164—165
Linear dependence 2
Linear independence 2
Linear transformations 3—8 10—16 22 35
Lorentz force 183
Lorentz gauge condition 135 181
Lorentz transformation 166—168 179
Lowering suffices 18
Manifold 29—33
MAP 29—33
Mass and energy 72 175 176
Mass, control knob 92
Mass, gravitational xi 71 91 186
Mass, inertial xi 71 91 186
Matrix notation 5 14
Maxwell's equations 56 181—182
Mercury, perihelion of xv 115—117
Metric in rotating frame 65—66
Metric, connection 45—48
Metric, Minkowski 54 164
Metric, Robertson — Walker 150
Metric, Schwarzschild 86—89 94
Metric, tensor 17—19 36 82
Metric, tensor field 36
Missing matter 157
Moment of inertia 20—23
Momentum 72 175 177
Newton's law of universal gravitation 63—64
Newton's laws of motion 59—60 163 176
Newtonian cosmology 158—160
Newtonian geodesic deviation 84
Newtonian orbit 110 115 130
Newtonian potential 63 82
Newtonian vertically falling particle 109
Notation xvi 2 3 44 54 71
Null cone 125—126 172
Null coordinate 91
Null curve 37
Null geodesic 58
Null vector 19 58 173
Olber's paradox 149
Orbits of particles 110—112
Orbits of photons 113—115
Order of tensors 12
Orthogonal vectors 20
Orthonormal basis vectors 21
Parallel transport 43
Parallelism 38—43
Particle motion in gravitational field 105—112
Perihelion advance xv 107 115—117
Photons, motion near star 113—115
Poincare transformations 166
Poisson's equation 85—86
Polarisation, electromagnetic waves 139—140
Polarisation, gravitational waves 137—141
Potential, electromagnetic 135 139 182
Potential, Newtonian 60—63 82
Preferred coordinates xiv
Principle of equivalence xi—xiii
Principle of general covariance xv 56
Products, tensor 9—11 133
Proper time xiii 56—57 71 96 98 101 105 106 150 165 170
Quotient theorem 13 77
Radar sounding xvi 98—100
Radiation from dumb-bell 144
Radiation, gravitational 132—147
Radius of orbit 111 120
Radius, Schwarzschild 123
Raising suffices 18
Rank of tensor see "Order of tensor"
Redshift 102—105
Ricci tensor 78 83
Riemann — Christoffel curvature tensor 77
Riemannian manifold 37
Robertson-Walker line element 52 150
Rotating reference system 64
Scalar (as type (0, 0) tensor) 12 72
Scalar field 35
Schwarzschild radius 123
Schwarzschild solution 63 86 89 94
Second moment of mass distribution 133 143
Simultaneity 170 174
Space, 3-dimensional 94 163
Spacelike coordinate 91
Spacelike vector 58 173
Spaces, tensor 9—15
Spaces, vector 1—9
Spacetime, curved 25—28 54—59 150
Spacetime, diagram 100 102 111 114 171—174
Spacetime, flat 25—28 54—55 163—164 173
Spectral shift xvi 100—105
Speed of gravitational waves 136
Speed of light (flat spacetime) 163
Speed of light (in gravitational field) 98 114
Speed, angular 122
Straightest lines 25—28 48—49
Stress-energy-momentum tensor for dust 90
Stress-energy-momentum tensor for fluid matter 73 75
Tachyons 58 186
Tangent space 33—37
Tangent vector 34
Tensor fields 33—37
Tensor product ( ) 9—11 133
Tensor, examples 14 20
Tensors of type (r, s) 12 77
Tensors, associated 19
Tensors, contraction of 15
Tensors, defined 11—12
Tensors, formed by differentiation 38
Tensors, mixed 12
Tensors, symmetric, skew symmetric 16—17
Tensors, transformations of 11 13 35
Test particle 60
Time in rotating frame 67
Time, coordinate xiii 71 94—97 98 101
Time, cosmic 150
Time, delay of, near star xvi 98—100
Time, dilation 67 170
Time, Newtonian 163
Time, proper xiii 56—57 71 96 98 101 105 106 165 170
Timelike coordinate 91
Timelike geodesic 58
Timelike vector 58 173
Total energy of universe 160
Transformations of basis vectors 3 4 8 11 35
Transformations of components 13 14 35
Transformations, Galilean 168 183
Transformations, gauge 134 181
Transformations, Lorentz 166—168 179
Transformations, Poincare 166
TT gauge 138
Unit vector 19
Universe, properties of 149
Vectors and vector spaces 1—5
Velocity, coordinate 72 98 109—110 175
Velocity, world 72 175
Wave equation 136 181
Wave, 4-vector 137 175
World lines 111 125 165 173
World velocity 72 175
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