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| Ïîèñê ïî óêàçàòåëÿì |
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| O'Neill B. — The Geometry of Kerr Black Holes |
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| Ïðåäìåòíûé óêàçàòåëü |
Kretschmann curvature 18
Kretschmann curvature, of Kerr spacetime 100
Kruskal domain 118—121 128—129
Kruskal extension of Schwarzschild spacetime 136
Lagrangian for geodesics 15—16
Levi — Civita connection 14
Lie bracket see “Bracket operation”
Lightcone see “Nullcone”
Lindquist, R.W. 121
Line-element 13
Line-element for Kerr spacetime see “Ken-metric”
Long horizons 119 124 130 172 174—175
Lorentz cylinder 174
Lorentz manifold 13
Lorentz metric 13
Lorentz vector space 25—31
m-principal null vector 318—319
Manifold 2
Map(ping), smooth 2
Mapping Lemma 23
Mass of a particle 34 35
Mass of Kerr spacetime 58
Matching map 21
Maximal Kerr spacetimes, bundle structure of 140—147
Maximal Kerr spacetimes, extreme 114
Maximal Kerr spacetimes, extreme, construction of 111—115
Maximal Kerr spacetimes, fast 109
Maximal Kerr spacetimes, parallelizability of 144
Maximal Kerr spacetimes, slow 137
Maximal Kerr spacetimes, slow, construction of 116—118 137—138
Maximal Kerr spacetimes, small extreme 168—169
Maximal Kerr spacetimes, small slow 168—170
Metric identities 60
Metric tensor 12
Midline 216
Minkowski space(time) 31 58—59
Minkowski, Hermann 31
Momentum see “Angular momentum” “Energy-momentum”
Multiplicity, of principal null vector 318
Multiplicity, of principal null vector, in terms of Weyl scalars 338
Neighborhood, coordinate 2
Neighborhood, tubular 45
Newman — Penrose formalism 333—341
Newman — Penrose formalism, curvature formulas in 339—340
Newtonian and relativistic gravitation 31—32 179
Nondegeneracy (of scalar product) 12
Null curve, vector field 33
Null curve, vector field, submanifold 46
Null subspace 29—31
Null tetrad (field), complex 332
Null tetrad (field), real 321
Null tetrad (field), real, associated with orthonormal basis 321
Null vector 27
Nullcone 27
Observer 36—39
Observer field 36
Observer field, Kerr 71—72
Observer, instantaneous 38
One-form 6 355—356
One-form, dual 11
Optical scalars (expansion, rotation, shear) 327—332
Optical scalars (expansion, rotation, shear), for Kerr spacetime 331
Optical scalars (expansion, rotation, shear), in Newman-Penrose formalism 335
Orbit manifold 168
Orbit types 209—211
Orbit types, exceptional: asymptotic 209
Orbit types, exceptional: crash-crash 209
Orbit types, exceptional: crash-escape 209
Orbit types, exceptional: spherical (stable, unstable) 20 211
Orbit types, regular: flyby 209
Orbit types, regular: interval-bound 209
Orbit types, regular: transit 209
Orbits of Kerr geodesics see also “Global trajectories”
Orbits of Kerr geodesics, direct 180
Orbits of Kerr geodesics, retrograde 180
Orientability 363
Orientability of the maximal Kerr spacetimes 144
Orientation of a manifold, by a 4-vector field 324—325 363—364
Orientation of a manifold, preserved [reversed] by a mapping 326—327 364
Orientation, of a vector space, by a (positively oriented) basis 303
Orientation,of a vector space, by a 4-vector 303
Orthogonal vectors 25
Orthonormal basis 26
Orthonormal expansion 26
Oval, in r-L plot 228—229 279—280
Pair symmetric (0, 4) tensor 298
Parallel translation 15
Parallelizable manifold 144
Particle lightlike 34—35
Particle material 34—35
PAST see “corresponding future references”
Penrose, Roger 181
Petrov types 313
Petrov types, algebraically special 314
Petrov types, criteria for 315
Petrov types, in terms of principal null directions 318—319
Petrov types, of Kerr spacetime 315—317
Petrov, A.Z. 313
Photon 34
Polar plane 68—69
Polar plane, global properties of 147—149 163
Polar plane, large 147
Pregeodesic 15
Principal null congruence abstract 327
Principal null congruence in Kerr spacetime 86
Principal null directions (or vectors) abstract 318
Principal null directions (or vectors) determined by curvature 325—326
Principal null directions (or vectors) in Kerr spacetime 88
Principal null geodesics 79—80 85—86
Principal null geodesics, exceptional 111
Principal null geodesics, first-integrals of 184—185
Principal null geodesics, in horizons 85—86 121 124
Principal null geodesics, in the axis 88
Principal null geodesics, ingoing 79
Principal null geodesics, ordinary 111
Principal null geodesics, outgoing 79
Principal plane 88 325
Product manifold 2
Proper time 34
r-L plots 214—222
r-L plots, configurations of (for timelike geodesics), barrier 229—231
r-L plots, configurations of (for timelike geodesics), bay 231—233
r-L plots, configurations of (for timelike geodesics), continents 223—224 226—227
r-L plots, configurations of (for timelike geodesics), lake 234—235
r-L plots, knobs in 228—229
Radial cordinate r 57—58
Radial cordinate r, extended over Kruskal domains 129
Radial cordinate r, extended through zero 62
Radial cordinate r, fails as KBL coordinate 121
Radial cordinate r, of a geodesic 207—214
Radial cordinate r, on maximal slow Kerr spacetime 139—140
Radial equation (r-equation) 183
Raising and lowering indices 16—17 311
Rest 37 39 71
Restphoton 83—87 120 130
Ricci curvature tensor 18 299
| Ricci-flat manifold 36
Riemannian curvature tensor 17—19
Riemannian manifold 12
Riemannian metric 12
Ring singularity 55 63
Ring singularity, as curvature singularity 100—102
Ring singularity, hitting, by geodesics see under “Geodesics”
Rotation see “Optical scalars”
Rotation coefficients 94 97
Rotation types of Kerr spacetimes extreme 61—62
Rotation types of Kerr spacetimes fast (rapidly rotating) 61—62
Rotation types of Kerr spacetimes slow (slowly rotating) 61—62
Rotational energy 202
Sachs criteria 320—322
Sachs equations 330 332 339
Sachs, R.K. 327
Scalar curvature 18
Scalar product 12 25
Scalar product, nondegeneracy criterion 25
Schwarzschild comparison (with Kerr spacetime), basic geometry 89—90
Schwarzschild comparison (with Kerr spacetime), circular photons 279
Schwarzschild comparison (with Kerr spacetime), connection forms 93—94
Schwarzschild comparison (with Kerr spacetime), curvature forms 99
Schwarzschild comparison (with Kerr spacetime), isometries 163
Schwarzschild comparison (with Kerr spacetime), Kruskal extensions 136
Schwarzschild comparison (with Kerr spacetime), metric tensors 59
Schwarzschild comparison (with Kerr spacetime), r-L plots 283
Schwarzschild spacetime (or black hole 55 57—59 61 72 73 102
Schwarzschild, Karl 31
Second fundamental form see “Shape tensor”
Second structural equation 52—53
Semi-Riemannian manifold 12
Separation (by a hypersurface) 46
Shape tensor 49
Shear see “Optical scalars”
Signature of a Lorentz vector space 26
Singularity see “Ring singularity and Curvature singularity”
Small Kerr spacetimes 168—170 176
Smooth (infinitely differentiable) function 2
Smooth (infinitely differentiable) manifold 2
Smooth (infinitely differentiable) mapping 2
Smooth (infinitely differentiable) tensor field 8
Spacelike curve, vector field 33
Spacelike submanifold 46
Spacelike subspace 29
Spacelike vector 27
Spacetime 33
Special relativity 31 36 39—41
speed of light 38—40
Sphere 2
Spherical coordinates 43—44
Spin coefficients 333
Spin coefficients, effect of tetrad change on 335—336
Stably bound orbit 211
Standard particle 244
Star-Kerr spacetime 106—108
Star-Kerr spacetime, comparison with Kerr-star space time 108—110
Static spacetime 36—37
Stationary limit 72
Stationary observer field 36—37
Stationary spacetime 37—38
Steinberg, Robert 225
Stoghianidis, E. 263
Structural equations 50—53
Submanifold 42—44
Submanifold, closed 43
Submanifold, spacelike, null, timelike 46
Submanifold, totally geodesic 48—49
Subspace (of a Lorentz vector space) spacelike, null, timelike 29
Symmetries of curvature 18
Tangent bundle 3
Tangent space 3
Tangent vector of curve 4
Tangent vector to a manifold 3
Tensor 8—12 16—17
Tensor at a point 12
Tensor components 10 11
Tensor contravariant 9
Tensor covariant 9
Tensor of type (0, 4) biskew 298
Tensor of type (0, 4) cyclically symmetric 298
Tensor of type (0, 4) pair-symmetric 298
Tensor of type (0, 4) tracefree 299
Tensor product 9
Tensor, type-changing of 16—17
Tetrad see “null tetrad”
Tetrad, expansion 334
Tetrad, reversal 333
Thorpe, John 313
Throat 69
Throat, geometry of 70 292—293
Time function T for Kerr coordinates 80 122
Time Machine 76—78
Time traveler 249
Time-orientation 33
Time-orientation, notation for reversal of 116
Timecone 28
Timecone, future see “futurecone”
Timelike curve, vector field 33
Timelike submanifold 46
Timelike subspace 29
Timelike vector 27
Totally geodesic submanifold 48—49
Tracefree tensor 299
Transversality 45
Tsoubelis, D. 263
Twin paradox 34
Two-four rule 215
Two-sided (and one-sided) hypersurfa 46
Type D curvature 313—315 318—319 322—327 343—344 see
Type D curvature, for Kerr metric 315—317
Type of a tensor 8
Unit vector 26
UNITS 351—353
Universal mapping property 299 361
VACUUM 36
Vector bundle 7
Vector field 4
Vector field, as differential operator 5
Vector field, complete 6
Vicious set 174—175
Violation of causality, chronology 74—75 174
Vishveshwara, C.V. 73
Vortical (timelike) geodesics 205 236—243
Weak Einstein convention 10
Wedge product of forms 355—356
Wedge product of vectors 361
Weyl conformal curvature tensor 301 302
Weyl conformal curvature tensor, for type D 322—327
Weyl conformal curvature tensor, in Newman-Penrose formalism 337
Weyl scalars 337
Weyl, Hermann 302
White hole 88 274 291
Wilkins, D.C. 224
Worldline 40
Zipper construction of maximal extreme Kerr spacetime 114
Zipper construction of maximal slow Kerr spacetime 137—138
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