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| Papapetrou A. — Lectures on general relativity |
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| Предметный указатель |
Action integral 118
Advance of the perihelion of a planet 75 76
Affine connection 19
Affine parameter of a geodesic 27
Algebraic classification of Weyl tensor 44 47 48
Algebraically special or general metrics 48
Amplitude of a shock wave 175 177
Angle formed by two vectors 32
Angular momentum of a stationary field 114—117
Angular momentum of Kerr solution 103 105
Antisymmetric tensors 9 10 11
Axial symmetry 104 114
Background metric 149
Bianchi identity 42
Bicharacteristics 174
Birkhoff theorem 70 101
Birkhoff theorem for Einstein — Maxwell field 137 140
Bivector 41
Bivector form of Weyl tensor 44 45
Bivector space 41 44
Black holes 91 92
Bondi coordinates see radiation coordinates
Bondi — Metzner — Sachs group 180
Cauchy problem 173
Characteristic surface 89 173
Characteristic surface, of Reissner — Nordstroem metric 143 148
Characteristic surface, surfaces of Kerr metric 107
Christoffel symbols 35 36
Closed spaces 194
Collapse, gravitational 85 91—93 96
Comoving coordinates 95—98
Conformal curvature tensor see Weyl tensor
Conformal transformation 43
Connection 18
Connection of a riemannian space 35
Connection, properties of connections 19
Conservation law of angular momentum 132—133
Conservation law of energy and momentum 96 128—131 134 135 159
Conservation law, laws related to Killing vectors 73
Constant curvature, space of 193
Contraction of a tensor 8
Contravariant form of metric tensor 34
Coordinate condition for linear approximation 111—112
Coordinate system adapted to a Killing vector 52 104
Coordinate transformation 5
Coordinate transformation, regular 5—6
Cosmological constant 62- 192
Cosmological principle 193
Cosmological problem 191
Covariant derivative 19 20—24
Covariant field equations 119
Curvature scalar 42
Curvature scalar, tensor contractions 29 42
Curvature scalar, tensor of a connected space 28
Curvature scalar, tensor of a riemannian space 40
De Sitter (cosmological) solution 192 197
Debever — Penrose equation 47
Deflection, gravitational of light rays 57 77—80 93
Densities, metrical 33
Densities, scalar 12
Densities, symmetry properties 12
Densities, tensor 11—12
Density of proper mass 95
Determinant of  33
Dicke experiment 55
Differentiation, covariant see covariant derivative
Differentiation, of a tensor field 15
Dipole structure of momentum distribution and angular momentum 115
Discontinuities in shock waves 170 171—172
Discontinuities, gravitational, local structure 174—176
Discontinuities, gravitational, propagation relations 174 176—177
Discontinuities, trivial and essential 173 174
Displacement vector 4
Distance in a riemannian space 31
Distortion see shear
Divergence 17
Doppler shift 85 193
Dust 95
Dynamical equation 150
Eddington — Finkelstein form of Reissner-Nordstrom metric 142—143
Eddington — Finkelstein form of Schwarzschild metric 87
Eigenvalue 44
Eigenvalues of Weyl tensor 45—46
Eigenvector 44
Einstein field equations in empty space 60
Einstein field equations with cosmological constant 61
Einstein field equations with matter term 60
Einstein Universe see static cosmological model
Einstein — Cartan theory 148
Einstein — Infeld — Hoffman (EIH) method see “astronomical” problem of motion
Einstein — Maxwell equations 134 135—137
Einstein — Strauss tensor 42
Einstein — Strauss theory see unified field theories
Electromagnetic field equations see Maxwell equations
Electromagnetic force density 135 149
Electrovacuum 135
Energy of a particle as measured by a given observer 81
Energy, total of a time-independent field 112 131—132
Eotvos experiment 55
Equations of motion in general Relativity 149—150
Equivalence principle 55
Euclidean space 31
Event horizon see horizon
Expanding Universe 193 197—198
expansion 186
Field equations derived from a variational principle 120 121—123 136—137
Five-dimensional theories see unified field theories
Flat space 29 43
Fluid without pressure see dust
Fock method see “astronomical” problem of motion
Freud superpotential 127
Friedmann cosmological solution 193 197
Geodesic coordinate system 37
Geodesic motion 56 58 70 156
Geodesic motion of dust particles 96 98
Geodesic null congruence 184
Geodesies of a connected space 26
Geodesies of a riemannian space 37 38
Geodesies of a riemannian space, minimal property 38—39
Geodesies of the Schwarzschild space, equations 70—71
Geodesies of the Schwarzschild space, first integrals 72
Geometrization of gravitational field 1 57
Gradient of a scalar 15
Gravitational collapse 91 92
Gravitational collapse of a cloud of dust 102 103
Gravitational constant, relativistic 61
Gravitational field 53
Gravitational field equations see Einstein field equations
Gravitational multipoles 167
Gravitational Poynting vector 162 164
Gravitational radiation 157 158
Gravitational radiation in the linear approximation 160—164
Gravitational radiation, positive energy 164 180 189
Gravitational radius of a body 74
Harmonic coordinate condition 159
Horizon of Kerr space 105 106—107
Horizon of Reissner — Nordstroem space 140 143
Horizon of Schwarzschild space 85 88
Hubble constant 198
Hubble effect 193
identities 42 68 123—128
Incompleteness of Kerr space 107
Incompleteness of Reissner — Nordstroem space 146
Incompleteness of Schwarzschild space 90
Inertial coordinate systems 1
Interior solution 92 95—96 140
Isometries 51
Isotropic form of Schwarzschild metric 94
| Isotropic stress tensor 95
Kaluzza — Klein theory see unified field theories
Kerr solution 103—107
Killing equation 51 63
Killing vectors 51 63 104
Killing vectors and conservation laws 73
Kronecker symbol, Kronecker tensor 6 7 21
Kruskal coordinates 85 90—91
Lagrangian 118
Lagrangian of Einstein — Maxwell field 136
Lagrangian of gravitational field 120 121
Levi-Civita tensor density 13 24
Lie derivative 48
Lie derivative, formulae for tensors 49—50
Linear approximation 108—112 159
Linearized field equations 109—110
Linearized field equations, reduced form 111
Mach's principle 59 191 192
Mapping, infinitesimal 48
Mapping, isometric 51
Mass, gravitational-inertial 55
Matter tensor 53
Matter tensor, trace of 54
Maxwell equations 17 112 134
Maxwell equations, stress-energy-momentum tensor 135
Mercury, advance of perihelion 76 77
Method of Newman — Penrose 187—189
Metric space 31
Metric space in bivector space 44 45
Metric space, tensor of a riemannian space 32
Minkowski space 31
Motion of test particles 58 149 151 152—157
Motion of the perihelion of a planet 75 76—77
New's function 181
Newman — Penrose method see method of Newman — Penrose
Newtonian theory of gravitation 53
Noether theorem 123
Nordstrom theory of gravitation 2 54
Normal form of radiative part of linearized metric 166
Normal form of Weyl tensor 47
Null surface see characteristic surface
Null tetrad see tetrad
Open spaces 194
Palatini equation 122
Parallel transport 24—26
Parallel transport along a closed path 28 29
Perfect fluid 95 195
Perihelion of a planet, motion of 75—77
Petrov classification of Weyl tensor 46
Phase of a shock wave 175 177
Photons (test particles of zero rest mass), equation of motion 82
Planets as test particles 74
Principal null vectors 47
Principle of equivalence 55—59
Principle of equivalence applied to proper frequencies 80
Product of tensors 8
Projection operator 164
Proper frequencies 80
Proper length of a curve 37
Pseudotensor of gravitational field 129 160
Pseudotensorial conservation laws 129 160
Radial geodesies of Reissner — Nordstroem metric 144—146
Radial null geodesies of Reissner — Nordstroem metric 143—144
Radial null geodesies of Schwarzschild metric 87—89
Radiation 158. See also gravitational radiation
Radiation coordinates 177—180
Red shift, cosmological 198
Red shift, formula for time-independent fields 83
Red shift, gravitational of spectral lines 80 84
Reissner — Nordstroem solution 137—140
Relativistic correction of Newtonian motion 74
Retarded action 158
Retarded solution of linearized field equation 112 162—163
Ricci tensor 42
Riemann tensor 40
Riemann tensor symmetry properties 40 41
Riemannian space 31
Rotation coefficients 183 184
Rotation of a vector 16
scalar 4
Scalar product of vectors 6 25 32
Schroedinger theory see unified field theories
Schwarzschild metric in comoving coordinates 101—103
Schwarzschild metric in radiation coordinates 179
Schwarzschild solution 66—70
Schwarzschild sphere 85
Shear 187
Shock waves 169 170
Shock waves, gravitational 158 169—177
Signature of the metric 35
Single pole test particle 151 154—157
Singular point 33
Singularity of Kerr metric 105
Singularity of Reissner — Nordstrom metric 142
Singularity of Schwarzschild metric 92
Singularity, coordinate or intrinsic 34
Space, metric 31
Space, Riemannian 31
Special relativity 1
Spherically symmetric metric 63—66 137 194
Spherically symmetric vector potential 137 138
Spin coefficients 184
Spinning test particles 156
Static cosmological model 192 196—197
Static fields 63 112
Stationary fields 51 114
Stress-energy-momentum tensor 53
Stress-tensor 95
Sum of tensors 8
Summation convention 6
Superpotential 127
Symmetric tensors 9 10
Tangent vector 5 38
Tensor 4 7
Tensor equations 4
Tensor field 15
Tensor, symmetric or antisymmetric in two indices 9 10
Test, particle 58 149
Test, particles, motion of 58 70 77 151 152
Tetrad components of a tensor 183
Tetrad, null 183
Tetrad, orthonormal 182
Tetrads 181—183
Time delay experiments 85
Tolman solution 96 99—103
Trace 9
Trace of matter Tensor 54
Trajectories; 3-dimensional of test particles 73 75—80
Transformation formulae for tensors 7
Transformation formulae for vectors 5 6
Twist 187
Unified field theories 147—148
Unified field theories, Einstein — Strauss and Schroedinger theory 148
Unified field theories, Kaluzza — Klein (5-dimensional) theory 147
Vaidya solution 103 107
Variational Principle 39 118—123
Vector, contravariant 4 5
Vector, covariant 6
Vector, potential, electromagnetic 112 134
Velocity; 4-dimensional 72
Velocity; 4-dimensional, macroscopic 95
Volume element, invariant in a riemannian space 33
Volume element, non-invariant 13 14
Weak gravitational fields 85 108 113
Weight of a tensor density 12
Weyl tensor 43 44—48
Weyl tensor, algebraic classification 47 48
White holes 103
“Astronomical” problem of motion 151 152
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