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Papapetrou A. — Lectures on general relativity
Papapetrou A. — Lectures on general relativity

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Название: Lectures on general relativity

Автор: Papapetrou A.

Язык: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 203

Добавлена в каталог: 25.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $g_{\lambda\mu}$      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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