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O'Neill B. — The Geometry of Kerr Black Holes
O'Neill B. — The Geometry of Kerr Black Holes



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Íàçâàíèå: The Geometry of Kerr Black Holes

Àâòîð: O'Neill B.

ßçûê: en

Ðóáðèêà: Ôèçèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: 1st edition

Ãîä èçäàíèÿ: 1995

Êîëè÷åñòâî ñòðàíèö: 381

Äîáàâëåíà â êàòàëîã: 04.04.2009

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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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