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| O'Donnel P. — Introduction to 2-Spinors in General Relativity |
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| Предметный указатель |
Product, inner, bilinear 2 10
Product, inner, non-degenerate 2 10
Product, inner, symmetric 2
Product, outer 15 23
Product, tensor 133
Quotient theorems 139
Rainich, G.Y. 92
Representation theory 1
Restricted Minkowski tetrad 3
Ricci identity 49 155
Ricci identity, spinor equivalent 50
Ricci rotation coefficients 54 106
Ricci scalar 92 157
Ricci spinor 44 107
Ricci spinor, dyad components 61 108
Ricci tensor 44 92 93 157 163
Ricci tensor, spinor equivalent 44
Ricci tensor, trace-free 45
Ricci — Lanczos equations 95 106
Ricci — Lanczos equations, spin coefficient form 107
Riemann space 154 161
Riemann space, geodesic of the 159
Riemann sphere 6—8
Riemann tensor 47 87 91 93 95 155
Riemann tensor, anti-self-dual 91 92
Riemann tensor, double dual 94
Riemann tensor, right-dual 43
Riemann tensor, self-dual 91
Riemann tensor, spinor equivalent 41 42
Riemann tensor, symmetries 156
Riemann tensor, ‘splitting’ of 93
Riemann — Lanczos equations 96
Riemann — Lanczos problem 99
Riemannian geometry 91 159
Rigid body mechanics 141
Rindler, W. 11 12
Sachs, R. 75 87
Scalar product see “Inner product”
Schwarzschild metric 117
Schwarzschild solution 168—170 173 175
Schwarzschild solution, static 176
Self-dual 32
Shear 87
Sirius B 176
Space-time 5
Spacelike vector 8
Spatial rotation see “Spin transformation”
Spatial rotation parameter see “Spin parameter”
Special linear group see “ \mathbb{C})$"/>”
Special relativity 5 144
Spin basis 11 20 104
Spin basis, non-normalised 54
Spin boost transformations 76
Spin coefficients 105
Spin coefficients, GHP form 78
Spin coefficients, under  and  70
Spin coefficients, under asterisk operation 73
Spin coefficients, under null rotations 65 66
Spin coefficients, under prime operation 72
Spin coefficients, unweighted 79
Spin coefficients, weighted 78 79
Spin coefficients, weighted, types of 79
Spin matrix 8
Spin parameter 68 76
Spin transformation 8 68
Spin, coefficients 53 118
Spin-and boost-weighted quantities see “Weighted quantities”
Spin-boost transformation, curvature spinor components 69
Spin-boost transformation, spin basis 68
Spin-boost transformation, spin coefficients 68
Spin-boost transformation, Weyl spinor components 69
Spin-space 10 13 20 27
Spin-vectors 4 7 9—11 13—15
Spin-vectors, fields 13
Spin-weight 81
Spinor commutation operators 48
Spinor covariant derivative 39
Spinor equivalent, anti-self-dual 32
Spinor equivalent, electromagnetic field tensor 31
Spinor equivalent, Lanczos tensor 100
Spinor equivalent, Levi — Civita tensor 32
Spinor equivalent, metric tensor 18 26
Spinor equivalent, self-dual 33
Spinor equivalent, symmetric valence two tensor 30
Spinor equivalent, world-vector 26
Spinor operations, complex conjugation 15
Spinor operations, Hermitian 27
Spinor operations, indices, raising and lowering 19
Spinor operations, see-saw 19
Spinor operations, skew-symmetrisation 22
Spinor operations, spinor decomposition 30 31
Spinor operations, symmetrisat ion 23
Spinor Ricci rotation coefficients 53
Spinorial objects 9
Spintensor 93 120
Square distance 158 168
| Stereographic coordinate 6
Stereographic projection 6
Stewart, J. 86
Takeno, H. 99
Tangent plane 129
Tangent space 129
Tangent vectors 129
Taylor, J.H. 75
Tensor, Einstein 94 158 162
Tensor, energy-momentum 92 146 162
Tensor, Lanczos 93 96 97 99
Tensor, metric 92 93 95 146 159 161
Tensor, Minkowski 99 146
Tensor, moment of inertia 142
Tensor, Ricci 92 93 157 163
Tensor, Riemann 91 93 95 155
Tensor, skew-symmetric 137
Tensor, symmetric 137
Tensor, transformation law 136 138
Tensor, Weyl 35 91 96
Tensor, Weyl, anti-self-dual 47
Tensor, Weyl, dual 47
Tetrad 1 20
Tetrad indices 62
Tetrad, left-handed 3
Tetrad, null 27 29 56 77
Tetrad, orthonormal 28 29
Tetrad, orthonormalisation conditions 2
Tetrad, right-handed 3
Thorne, K.S. 12
Timelike vector 2
Timelike vectors 5
Tod, K.P. 12
Torsion 40
Trace 136
Transformation, antipodal 12
Transformation, conformal 7
Transformation, holomorphic 7
Transformation, of phase 8
Transformation, spin 8
Transvection 15
Two-form 10
Udeschini, E.B. 99
Univalent spinors 15
Universal gravitational constant 166
Unweighted operators 80
Unweighted quantities 77
Valence, spinor 15
Valence, tensor 133
Variational Principle 92 179
Vector space 1 10 129
Vectors 2
Vectors, angular momentum 141
Vectors, angular velocity 141
Vectors, contravariant 132
Vectors, covariant 132
Vectors, null 2 28 150
Vectors, null, future-pointing 2 8 27
Vectors, null, past-pointing 2 27
Vectors, orthogonal 150
Vectors, spacelike 2 8 28 150
Vectors, tangent 129
Vectors, timelike 2 28 150
Vectors, timelike, future-pointing 2
Vectors, timelike, past-pointing 2
Velloso, A.L. 115
Walker, M. 86
Weighted differential operators, commutation relations 83
Weighted differential operators, conjugated 82
Weighted operators 80
Weighted quantities, boost-weight 77
Weighted quantities, spin-weight 77
Weighted quantities, type 77
Weighted quantities, {p, q}-scalar 77
Weighted scalars 79
Weighted scalars, product of 80
Weighted spin coefficients 79
Weyl scalars 61
Weyl spinor 33 36 47 50
Weyl spinor, classification of 34
Weyl spinor, dyad components 61 105
Weyl tensor 35 91 96
Weyl tensor, anti-self-dual 47
Weyl tensor, dual 47
Weyl tensor, left-dual 47
Weyl tensor, right-dual 47
Weyl — Lanczos equations 96 115 118
Weyl — Lanczos equations, in GHP form 114
Weyl — Lanczos equations, Petrov type D space-times 117
Weyl — Lanczos equations, Petrov type III space-times 116
Weyl — Lanczos equations, Petrov type N space-times 116
Weyl — Lanczos equations, Petrov type O space-times 115
Weyl — Lanczos equations, spin coefficient form 106
Weyl — Lanczos equations, spinor form 102 103
Weyl — Lanczos problem 99
Wheeler, J.A. 12
Zund, J.D. 106
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