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| O'Donnel P. — Introduction to 2-Spinors in General Relativity |
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| Предметный указатель |
 8 24 64
Abstract index notation 11 14—16
Affine connexion 92 152
Affine Minkowski space 127
Affine parameter 160
Algebraically general 34 36 87
Algebraically special 34 36 87 118
Angular momentum vector 141
Angular velocity vector 141
Anti-celestial sphere 6
Anti-self-dual 32
Antipodal transformation 12
Asterisk operation 73
Bampi, F. 99
Basis 17
Basis, complex null 52
Basis, dual 17 52
Basis, natural 129 131 133
Basis, orthonormal 3 105 146
Basis, spinors 20
Basis, vectors 1
Bianchi identities 50 87 92 158
Bianchi identities, contracted 51 158
Bianchi identities, GHP form 85
Bianchi identities, spin coefficient form 62
Bianchi identities, spinor equivalent 51
Bivalent spinor 16 23
Bivector 31
Bondi, H. 75
Boost see “Lorentz boost”
Boost parameter 68 76
Boost-weight 81
Canonical decomposition of symmetric spinors 33 34
Canonical decomposition of the Weyl spinor 36
Carmeli, M. 1
Cartan, E. 1
Caviglia, G. 99
Celestial sphere 5
Chart 128 130 131 133
Christoffel symbols 49 92 148 152
Classical mechanics 140
Commutation relations 58 119
Complex conjugate, spinor basis elements 22
Complex conjugation of spinor components 15
Complex field 10
Complex null basis 52
Complex plane 6
Complex plane, extended 6
Conformal transformation 7
Conjugated weighted differential operators 82
Connexion coefficients 148
Conservation of energy 145
Conservation of linear momentum 145
Conservation of mass 145
Contracted Bianchi identities 51
Contracted Bianchi identities, GHP form 85
Contraction 15 136
Contravariant vector field 158
Contravariant vectors 132
Coordinate neighbourhood 128
Coordinate transformation 131
Cosmological constant 45
Cosmological term 163
Covariant derivative 151
Covariant derivative, axioms 152
Covariant derivative, properties 39
Covariant derivative, spinor 39
Covariant vectors 132
Curvature scalar see “Ricci scalar”
Curvature spinors 42 47 49 59
Curvature tensor see “Riemann tensor”
Cvitanovic, P. 14
Cyclic condition 101
Deflexion of light 173 174
Dirac, equation for the electron 93
Dirac, Scissors Problem 12
Directional derivatives see “Intrinsic derivatives”
directions 5
Directions, future-pointing, null 5 76
Directions, future-pointing, timelike 5
Directions, past-pointing, null 5
Directions, past-pointing, timelike 5
Directions, principal null 31 33—36 87 118
Directions, spacelike 6
Directions, timelike 6
Divergence 146
Dual anti-self- 32
Dual basis 17 132
Dual space 15 132
Dual tangent space 132
Dual, basis 52
Dual, left- 32
Dual, self- 32
Dummy indices 17 131
Dyad 20
Dyad, components 52
Edgar, S.B. 99
Einstein field equations 45 75 92 163 166
Einstein field equations, spinor equivalent 45
Einstein summation convention 1 135
Einstein tensor 52 94 158 162 163
Einstein tensor, spinor equivalent 45
Einstein — Cartan — Sciama — Kibble theory 40
Einstein, A. 75 91 92
Electromagnetic field tensor 31 35
Electromagnetic spinor 32 33
Electromagnetic spinor, classification of 34
Empty space field equations 45
Energy-momentum tensor 45 92 146 162
Epsilon spinor see “Levi — Civita spinor”
Equation of continuity 145
Euclidean space 6 128 130
Euler — Lagrange equations 161 170
Euler’s equation 145
Event in space-time 127 128
Field, gravitational 162
Field, scalar 142
Field, scalar, gradient 143
Field, spinor 80
Field, tensor 80 142
Field, tensor, components 142
Field, vector 142
Flag plane 8—10
Flagpole 8 10
Geodesic 161
Geodesic coordinate system 148
Geodesic equation 159
Geodesic, null 163
Geodesic, timelike 163 165 170
Geroch — Held — Penrose formalism see “GHP formalism”
Geroch, R. 76
GHP field equations 82
GHP formalism 75 77
Goldberg — Sachs theorem 118
Goldberg, J.N. 87
Gravitational field 162
Gravitational field, static 164 168
Gravitational radiation problem 75
Gravitational red shift 175 176
Gravitational spinor see “Weyl spinor”
Gravitational waves 75
Held, A. 76 86
Hermitian matrix 24
Holomorphic transformation 7
Homomorphism, and L(4) 24
Huggett, S.A. 12
Hulse — Taylor binary pulsar 75
Hulse, R.A. 75
Hyperplane 5 6
Illge, R. 99
| Indices, contravariant 15 134
Indices, covariant 15 134
Indices, dummy 17
Indices, numerical 1 17 49
Indices, tetrad 62
Infeld-van der Waerden symbols 24—26
Inner product 2 15 136
Intrinsic derivatives 56 80 117
Jacobian 127 132
Kasner, E. 124
Kennedy, A.D. 14
Kinnersley null tetrad 117
Kinnersley, W. 117
Kronecker delta see “Kronecker symbol”
Kronecker spinor 53
Kronecker symbol 19 20 26 136
L(4) 24 64
Lagrange multipliers 92 93
Lagrange multipliers, trace 93
Lagrange multipliers, trace-free 93
Lagrangian 92—94
Lagrangian, tensor, local 99
Lanczos 96
Lanczos coefficients 105 114—117 119
Lanczos coefficients,  and  112
Lanczos coefficients, asterisk operation 113
Lanczos coefficients, null rotations 110
Lanczos coefficients, prime operation 113
Lanczos coefficients, spin boost transformation 111
Lanczos potential see “Lanczos tensor”
Lanczos spinor 99 101
Lanczos spinor, symmetry properties 102
Lanczos tensor 93 96 97 99
Lanczos tensor, spinor equivalent 100
Lanczos, C. 91 120
Lanczos, canonical variables 93
Lanczos, coefficients 104
Lanczos, cyclic condition 93
Lanczos, divergence-free 97 103
Lanczos, gauge conditions 97 101
Lanczos, trace-free 97
Left-dual 32
Levi — Civita spinor 11 16 18 19 23 32
Levi — Civita tensor 32
Liebniz’s law 40
Linearity 10
Lorentz boost 64 67 109 117
Lorentz group 64 76
Lorentz transformations 64
Lorentz, factor 144
Lorentz, group 24
Lorentz, scalar product 146
Lorentz, transformations 3
Lorentz, transformations, active 3 4
Lorentz, transformations, passive 3
Lorentz, transformations, restricted 3
Lorentzian metric 1
Lorentzian signature 150 161
Maher, W.F. 106
Malin, S. 1
Manifold, differentiate 128 146
Manifold, differentiate, four-dimensional 128 131 150
Manifold, differentiate, n-dimensional 128 131
Manifold, differentiate, one-dimensional 130
Manifold, differentiate, two-dimensional 128 130 131
Manifold, Euclidean 140
Manifold, Riemannian structure 154
Manifold, tangent space 131
Massa, E. 99
Matrix, hermitian 24
Matrix, Pauli spin 24
Matrix, spin 8
Maxwell spinor see “Electromagnetic spinor”
Mercury, perihelion of 173
Metric tensor 92 93 95 146 159 161
Minkowski coordinates 2 3 28
Minkowski geometry 127
Minkowski space 1 20 36
Minkowski space, affine 127
Minkowski space, non-singular 2
Minkowski space, time-orientation 2 3 27
Minkowski tensor 99 146 148
Minkowski tetrads 2 3
Minkowski tetrads, improper 3
Minkowski tetrads, orthochronous 2 3
Minkowski tetrads, proper 3
Minkowski tetrads, restricted 3
Misner, C.W. 12
Modified GHP formalism 86
Modified GHP operators 86
Moment of inertia tensor 142
Multivalent spinors 15
Natural basis 133
Natural basis vectors 129 131
Newman — Penrose field equations see “NP field equations”
Newman — Penrose spin coefficient, formalism see “NP formalism”
Newman, E. 52
Newtonian theory 164
Newton’s gravitational constant see “Universal gravitational constant”
Non-normalised spin basis 54
Novello, M. 115
NP field equations 59 60
NP formalism 52
Null cone 5—8
Null curve 160
Null directions 35
Null flag 8 9 13
Null geodesic 163
Null geodesies, shear-free 87
Null rays 5
Null rotations, Lanczos coefficients 110
Null rotations, spin coefficients 65
Null rotations, with 1 fixed 65
Null rotations, with 1 fixed, curvature spinor components 65
Null rotations, with 1 fixed, spin basis 65
Null rotations, with 1 fixed, Weyl spinor components 66
Null rotations, with n fixed, curvature spinor components 67
Null rotations, with n fixed, spin basis 66
Null rotations, with n fixed, spin coefficients 66
Null rotations, with n fixed, Weyl spinor components 67
Null tetrad 27 29 77 104
Null vectors 2 5 28
Orbiting planet 170
Orientation 3
Orthochronous Lorentz group 64
Orthonormal 146
Orthonormal basis 105
Orthonormal tetrad 28 29
Orthonormalisation conditions 20 28 29
O’Donnell, P. 117
Pagani, E. 99
Particle, four velocity 142 165
Particle, world line 142
Pauli spin matrices 24
Payne, W.T. 10
Penrose, R. 11 12 14 52 76
Petrov classification 34 35
Petrov type 36
Petrov type, algebraically general 36
Petrov type, algebraically special 36
Petrov type, degenerate 36
Petrov type, null 36
Poisson’s equation 162 166
Preferred parameter 160
Prime operation 71 77
Principal null directions 31 33—36 87 118
Principal spinors 34 36
Principle of covariance 150
Principle of equivalence 149 150 162
Product, inner 2 10 15 136
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