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

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Ќазвание: The Geometry of Kerr Black Holes

јвтор: O'Neill B.

язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 1st edition

√од издани€: 1995

 оличество страниц: 381

ƒобавлена в каталог: 04.04.2009

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ѕредметный указатель
$\vartheta$-equation      183
4-velocity      35
Acceleration      15
Achronal set      171Ч172
Action (of a Lie group      6Ч7
Allowed region, in an r-L plot      214
Analytic function      8
Analytic manifold      8
Angle function A for Kerr coordinates      80 122
Angular momentum of a geodesic around the Kerr axis      179
Angular momentum, per unit mass, of Kerr spacetime      58
Asymptotic flatness      59
Axial symmetry      59
Axis (of Kerr spacetime)      63 68
Axis (of Kerr spacetime), abstract      140 143
Axis (of Kerr spacetime), geometry of      87Ч88 102
Backward isometry      59 110 152Ч154 155Ч160 162Ч163
Barrier, in an r-L plot      230
Basis Hodge      303
Basis orthonormal      26
Basis positively oriented      303
Basis Theorem      3
Bianchi identity      19 341
Bianchi identity, in Newman Ч Penrose formalism      341Ч342
Biskew (0, 4) tensor      298
Bivector      360
Bivector decomposable      362
Bivector principal null      318
Black holes      see under УSchwarzschild and KerrФ
Bound orbit      see under УOrbit types and Global trajectoriesФ
Boyer Ч Lindquist (co)frame field      90Ч91
Boyer Ч Lindquist (co)frame field, brackets      96
Boyer Ч Lindquist (co)frame field, connection forms      92
Boyer Ч Lindquist (co)frame field, covariant derivatives      95
Boyer Ч Lindquist (co)frame field, curvature forms      98
Boyer Ч Lindquist (co)frame field, signs for      90 92
Boyer Ч Lindquist blocks      65Ч67
Boyer Ч Lindquist blocks, canonical imbedding of      82
Boyer Ч Lindquist blocks, causal properties of      75Ч78
Boyer Ч Lindquist blocks, incompleteness of block III      101
Boyer Ч Lindquist blocks, stationary properties of      70Ч72
Boyer Ч Lindquist blocks, visualization      63
Boyer Ч Lindquist coordinates      57
Boyer Ч Lindquist coordinates, failure at horizons      74
Boyer Ч Lindquist coordinates, metric identities for      60
Boyer Ч Lindquist polynomial      282
Boyer, R.H.      121
Bracket operation (Lie bracket)      5
Bracket operation (Lie bracket), for the Boyer Ч Lindquist vector fields      96
Bracket operation (Lie bracket), in Newman Ч Penrose formalism      334
Brans, Carl      348
Bundle structure of Kerr spacetime      140Ч144
Caesar, Julius      56
Canonical frame      323
Canonical imbedding of blocks      82
Canonical Kerr vector fields      60 68
Cartan computations, for the Boyer Ч Lindquist frame field      90Ч99
Cartan computations, in general      49Ч55
Carter band, in an r-L plot      236
Carter constant $\mathcal{K}$      183
Carter constant $\mathcal{K}$ and $\mathcal{Q}$ and approach to the ring singularity      201
Carter constant $\mathcal{K}$ and $\mathcal{Q}$, effect on forbidden regions      217
Carter constant $\mathcal{K}$ and $\mathcal{Q}$, effect on latitudinal motion      203Ч207
Carter constant $\mathcal{K}$ and $\mathcal{Q}$, general properties of      186Ч188
Carter constant $\mathcal{Q}$      188
Carter's (first-integral) theorem      183
Carter's (first-integral) theorem, proof of      357Ч359
Carter, Brandon      78 183 288
Causal (nonspacelike) vector      29
Causal character of a curve, vector field      33
Causal character of a submanifold      46
Causal character of a subspace      29
Causal character of a vector      27
Causal character of Boyer Ч Lindquist coordinate vector fields      66 70Ч72 78
Causal character of the canonical vector fields      66Ч67 see УNullФ УSpacelikeФ
Causal spacetime      75
Causality      74Ч75 171
Central sphere      69 145
Chandrasekhar, S.      349
Christoffel symbols      15
Chronological future [past] set      171
Chronological spacetime      75 174
Chronology      171
Chronology of Kerr spacetimes      171Ч176
Circular coordinate      7Ч8
Closed submanifold      43
Coframe field      11
Colatitude $\vartheta$      43Ч44
Colatitude $\vartheta$, as Boyer-Lindquist coordinate      57Ч58
Colatitude $\vartheta$, as coordinate of a geodesic      201Ч207
Comparison of Schwarzschild and Kerr spacetimes      see УSchwar schild comparisonФ
Complete vector field      6
Components of tensors      10 11
Configuration of an r-L plot      see under Уr-L plotФ
Conformal flat spacetime      314
Congruence      45 see
Connection forms      50Ч52
Connection forms for the Boyer Ч Lindquist frame field      see under УBoyer Ч LindquistФ
Conservation lemma      20
Continents, in an r-L plot      223
Contraction of tensors      11Ч12 17 299 332Ч333
Coordinate function      2
Coordinate neighborhood      2
Coordinate one-form      6
Coordinate system      2
Coordinate vector      3 5
Covariant derivative      14Ч15
Covariant derivative in Newman Ч Penrose formalism      334
Covariant derivative of Boyer Ч Lindquist vector fields      94Ч95
Covector      6
Crossing spheres      119 121 130 135 138 140 146
Curvature form      52
Curvature of Kerr spacetime, Cartan computation      96Ч100
Curvature of Kerr spacetime, Newman-Penrose expression      3
Curvature singularity      101
Curvature transformation      300
Curvature, abstract      298
Curvature, Gaussian      19 54
Curvature, in Newman-Penrose terms      338Ч340
Curvature, Kretschmann      18
Curvature, relativistic significance of      35Ч36
Curvature, Ricci      18
Curvature, Riemannian      17Ч19
Curvature, scalar      18
Curvature, sectional      18
Curvature, symmetries of      18
Curvature, Weyl conformal      301
Curve      4
Cyclic symmetry      298
Deformation retract      164
Diffeomorphism      3
Differential forms      6 355Ч356
Differential map      4
Differential of a function      6
Dimension of a manifold      2
Discriminant polynomial      215 217Ч222
distribution      44Ч45
Distribution, integrability of      45
Dual basis (or coframe)      11
e-Q chart      219Ч220
Effective energy, of a geodesic      214
Effective potential, for axial geodesics      254
Effective potential, for polar geodesics      263
Effective potential, in the $\vartheta$-equation      201Ч202
Einstein manifold      308 311
Einstein summation convention (weak)      10
Einstein, Albert      31 33 35
Energy extraction from a black hole      181Ч182
Energy, of a particle in Kerr spacetime      179
Energy-momentum 4-vector      35
Equator (equatorial plane)      68 146Ч147
Equatorial geodesics      272Ч287
Equatorial geodesics, circular null      277Ч278
Equatorial geodesics, circular timelike      282Ч283
Equatorial geodesics, in r<0      273Ч274
Equatorial geodesics, longitudinal motion of      283Ч284
Equatorial geodesics, null      276Ч279
Equatorial geodesics, spacelike      285Ч286
Equatorial geodesics, timelike      279Ч283
Equatorial isometry      68
Ergosphere      72Ч73 181
Escape energy      211
Euclidean space      2
Euler equations      16
Event      32
Event horizon      86Ч87
expansion      see under УOptical scalarsФ
Extension of Kerr spacetimes      57
Extension of manifolds by coordinates      20Ч21
Extention of Kerr spacetimes across r=0      62
Extention of Kerr spacetimes over the axis      64
Extention of Kerr spacetimes, plan for      105 see
Extention of manifolds by gluing      21Ч25
Exterior derivative      356
Exterior of Kerr spacetime      66
Exterior product of forms and of vectors      see Уwedge productФ
Exterior product of vector spaces      299 361Ч364
Fiber bundle      7
Fiber spheres      144
Fiber spheres in horizons      145Ч146
First structural equation      50
First-integrals      178Ч179 183
First-integrals as coefficients of the polynomial R(r)      208
First-integrals effect on orbits      222Ч235
Flat manifold      36
Flow      6
Flyby orbit      see under УOrbit types and Global trajectoriesФ
Foliation      45
Forbidden region, in an r-L plot      214
Frame field      10Ч11
Frame field, Boyer Ч Lindquist      see under УBoyer-LindquistФ
Frame field, orthonormal      17
Frobenius' Theorem      44 356
Fundamental groups of Kerr spacetimes      165 167 170
Future set      see УChronological future setФ
Future [past] complete geodesic      111
Future [past] side      172
Future-pointing      33
Futurecone      33
g-null      318
General relativity, introduction to      31Ч42
Geodesic completeness      15
Geodesic completeness modulo the ring singularity      189
Geodesics      15Ч16 48 334
Geodesics complete      111
Geodesics in Kerr spacetime, axial      250Ч255
Geodesics in Kerr spacetime, equations for: Colatitude equation ($\vartheta$-equation)      183
Geodesics in Kerr spacetime, equations for: Coordinate integral equations      190 191
Geodesics in Kerr spacetime, equations for: First-order equations for longitude and time      181 190
Geodesics in Kerr spacetime, equations for: Radial equation (r-equation)      183
Geodesics in Kerr spacetime, extensions of, across horizons      196Ч200
Geodesics in Kerr spacetime, extensions of, through a Boyer-Lindquist block      195
Geodesics in Kerr spacetime, hitting the ring, singularity      101
Geodesics in Kerr spacetime, hitting the ring, via the equator      288
Geodesics in Kerr spacetime, in horizons      255Ч262
Geodesics in Kerr spacetime, initial data for      185
Geodesics in Kerr spacetime, polar      262Ч272
Geodesics in Kerr spacetime, regular      189
Geodesics in Kerr spacetime, with Q=0      287Ч291 293 see УFirst-integralsФ УGlobal УPrincipal
Geometric units      351Ч353
Global trajectories, of Kerr geodesics      243Ч250
Global trajectories, of Kerr geodesics, for standard particles      244
Global trajectories, of Kerr geodesics, timelike bound orbits: in block I      247
Global trajectories, of Kerr geodesics, timelike bound orbits: in block III      247
Global trajectories, of Kerr geodesics, timelike bound orbits: large      248Ч249
Global trajectories, of Kerr geodesics, timelike flyby orbits: exterior      245
Global trajectories, of Kerr geodesics, timelike flyby orbits: in block III      245
Global trajectories, of Kerr geodesics, timelike flyby orbits: long      245Ч247
Global trajectories, of Kerr geodesics, timelike transit orbit      249Ч250
Gluing data      21
Gluing of manifolds      21Ч25
Goldberg Ч Sachs theorem      345Ч348
Hausdorff condition (for gluing)      23Ч24
Hitting the ring singularity      see under УGeodesics in Kerr spacetimeФ
Hodge basis      303
Hodge double indices      304 310
Hodge identity      304
Hodge star operator      303Ч308
Hodge star operator, as complex structure      305
Hodge star operator, in complex scalar product      306
Homotopy equivalence      164
Homotopy type      164
Homotopy type of extreme Kerr spacetime      168
Homotopy type of fast Kerr spacetime      164Ч165
Homotopy type of slow Kerr spacetime      166Ч168
Homotopy type of small Kerr spacetimes      168Ч170
Horizon function $\Delta$      58 62
Horizon sphere      145
Horizon, in Kerr spacetime      58 62Ч63
Horizon, in Kerr spacetime, as one-way membrane      84 172
Horizon, in Kerr spacetime, crossing, by geodesics      196Ч200
Horizon, in Kerr spacetime, geometry of      83Ч85
Horizon, in Kerr spacetime, long      see УLong horizonФ
Hypersurface      42Ч43 45Ч46 48
Hypersurface, achronal      171
Hypersurface, one-and two-sided      46
Hypersurface, separating      46
Hypersurface-orthogonal vector field      48 71 356
Index of a scalar product      26
Inextendibility of Kerr spacetimes      293Ч295
Inner product      12
Instantaneous observer      38
Integral curve      5
Integral manifold      44Ч45
Isometries of Boyer Ч Lindquist blocks      149Ч154
Isometries of extreme Kerr spacetime      155Ч158
Isometries of Kruskal domains      158Ч160
Isometries of slow Kerr spacetime      161Ч163
Isometry      13Ч14 48
Jacobi identity      5
KBL coordinates      121Ч130
KBL coordinates, related to Boyer Ч Lindquist coordinates      131Ч132 137
Kerr black hole      see also УKerr spacetimeФ
Kerr black hole, overview      55Ч56
Kerr black hole, physical properties summarized      102Ч103
Kerr exterior (block I)      66
Kerr metric on      131 134Ч135
Kerr metric tensor (or line-element), compared with Minkowski and Schwarzschild metrics      58
Kerr metric tensor (or line-element), in Boyer Ч Lindquist coordinates      58Ч59
Kerr metric tensor (or line-element), in Boyer Ч Lindquist coordinates, alternative formulation of      91
Kerr metric tensor (or line-element), in KBL coordinates      134Ч135
Kerr metric tensor (or line-element), in Kerr-star coordinates      81
Kerr metric tensor (or line-element), in star-Kerr coordinates      107
Kerr metric tensor (or line-element), on Kruskal domains      131Ч135
Kerr metric tensor (or line-element), on the axis      64Ч65
Kerr metric tensor (or line-element), Petrov type D character of      315Ч317
Kerr observers      71Ч74
Kerr patch      114 138
Kerr spacetime, maximal analytic extensions of      see УMaximal Kerr spacetimesФ
Kerr spacetime, slow, extreme, fast      see УRotation typesФ
Kerr spacetime, working definition of      67Ч68
Kerr, Roy      31
Kerr-Newman metric      61
Kerr-star spacetime      79Ч83
Kerr-star spacetime, definition      82
Killing isometry (group)      149Ч150
Killing orbit      69
Killing vector field      19Ч20 48
Killing vector field on Kerr spacetime      59 68 69 70Ч71 155
Kinnersley, William      344
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