Chandrasekhar S. — The Mathematical Theory of Black Holes :: Электронная библиотека попечительского совета мехмата МГУ

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Chandrasekhar S. — The Mathematical Theory of Black Holes

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Название: The Mathematical Theory of Black Holes

Автор: Chandrasekhar S.

Аннотация:

This volume has become one of the modern classics of relativity theory. When it was written in 1983 there was little physical evidence for the existence of black holes. Recent discoveries have only served to underscore the elegant theory developed here, and the book remains one of the clearest statements of the relevant mathematics.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1983

Количество страниц: 668

Добавлена в каталог: 03.04.2009

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Предметный указатель

$\mathscr{D}_{n},\ \mathscr{D}_{n}^{+}$       175 383
$\mathscr{D}_{n},\ \mathscr{D}_{n}^{+}$ , lemmas concerning      383—84
$\mathscr{L}_{n},\ \mathscr{L}_{n}^{+}$       175 383
$\mathscr{L}_{n},\ \mathscr{L}_{n}^{+}$ , lemmas concerning      383—384
$\mathscr{R}$ -Function      464 465
$\mathscr{R}$ -Function for a=0      501
$\mathscr{R}$ -Function, differential equation for      469 488
$\mathscr{R}$ -Function, tables of      626 627 629 630
$\mathscr{S}$ -function      466
$\mathscr{S}$ -function, differential equation for      470 489
$\mathscr{S}$ -function, for a=0      501
$\mathscr{S}$ -function, tables of      628 631
Adjoint, differential systems      153
Adjoint, differential systems, reducibility of      152
Affine connection      16 see
Area theorem      374 524 see
Asymptotic behaviours of Maxwell scalars      258 409 417—18
Asymptotic behaviours of metric functions      70 92 289 592
Asymptotic behaviours of Teukolsky functions      417 518
Asymptotic behaviours of Weyl scalars      195—196 256 518 522
Axial perturbations      142
Axial perturbations for Reissner — Nordstroem space-time      228
Axial perturbations for Schwarzschild space-time      143
Axial perturbations, expressed in terms of polar perturbations      162 237
Axisymmetric perturbations of space-times      140 see "Perturbations
Axisymmetric perturbations of space-times, variational formulation of      603
Axisymmetric space-times      see "Non-stationary axisymmetric space-times" "Stationary
Bardeen n Press n Teukolsky inequality      371
Barrier penetration, problem of      163 428 see "Problem
Bases for forms      6
Bases for vector space      5
Basis vectors      6 see
Basis vectors in Newman — Penrose formalism      41
Basis vectors in tetrad formalism      35
Bianchi identities in Newman — Penrose formalism      48
Bianchi identities in Newman — Penrose formalism, contributions to, by Maxwell tensor      53
Bianchi identities in perturbation theory      606
Bianchi identities in tetrad formalism      39
Bianchi identities, already linearized      175 241 431 581
Bianchi identities, definition      25 26
Bianchi identities, linearized      447
Bianchi identities, number of independent      33
Black-hole solutions, stability of      199 262 620
Black-hole solutions, stability of, type-D character of      63 135 238 300 596
Black-hole solutions, stability of, variational formulation      614
Bracket notation      442
Calculus of forms      10
Canonical basis      7
Cartan's equations of structure      22 23
Cartan's equations of structure, explicit forms for special cases      75 601
Carter's theorem as special case of Robinson's theorem      298
Carter's theorem, derived from perturbation theory      609
Cauchy horizon      205
Cauchy horizon of Kerr black-hole      313
Cauchy horizon of Reissner — Nordstroem black-hole      214
Cauchy horizon of Reissner — Nordstroem black-hole, crossing of      265 270
Christoffel connection      29
Christoffel connection, consequences of      30
Colon derivative      74 81 598
Commutation relations      38 see
Commutation relations in Newman — Penrose formalism      45
Commutation relations, linearized      448
Conjugate metrics      276 285 572
Conjugation, operation of, for axisymmetric space-times with electromagnetic fields      572
Conjugation, operation of, for axisymmetric-vacuum space-times      276
Connection one-form      17
Connection one-form, derived from a metric      28
Connection one-form, special cases      75 598
Conversion coefficient      261
Cosmic censorship      375
Cotton — Darboux theorem      70
Covariant differentiation of spinor fields      539
Covariant differentiation of tensor fields      16
Curvature      21
Curvature forms      21 77 601
Cyclic identity      26 290
Differential forms      7
Differential geometry, definitions      3—10 see
Dirac's equation      543
Dirac's equation in Kerr geometry      544
Dirac's equation in Newman — Penrose formalism      543
Dirac's equation, conserved current in      553
Dirac's equation, energy-momentum spinor for      559
Dirac's equation, reduction to one-dimensional wave-equations      553
Dirac's equation, separation of in oblate-spheroidal coordinates, in flat space      555
Dirac's equation, separation of, in Kerr geometry      546 561
Directional derivatives      36
Directional derivatives in Kerr space-time      383
Directional derivatives in Schwarzschild space-time      174
Distorted black-holes      583
Distorted black-holes, conditions for equilibrium of      586
Dual basis      6
Dual transformations      185 199 270
Dual transformations, condition for occurrence      186 246
Dual transformations, generalized versions      505
Duality transformation      590
Dyad formalism      538
Dynamical equations for non-stationary axisymmetric perturbations      608
Dynamical equations for quasi-stationary axisymmetric perturbations      610 611
Eccentricity      103
Eccentricity, imaginary      111 115
Einstein field-equations      34
Einstein field-equations, explicit forms for axisymmetric space-times      274—277
Einstein field-equations, explicit forms for non-stationary axisymmetric space-times      601—602
Einstein field-equations, explicit forms for spherically-symmetric space-times      86
Einstein tensor      31 see
Einstein tensor, components of, for non-stationary axisymmetric space-times      141 142 602
Einstein tensor, components of, for stationary axisymmetric space-times      274 275
Einstein — Maxwell equations, explicit forms for, an assemblage of black holes      588 589—91
Einstein — Maxwell equations, explicit forms for, stationary axisymmetric space-times      564
Einstein — Maxwell equations, explicit forms for, stationary axisymmetric space-times, reduction to standard forms      566
Einstein — Maxwell equations, explicit forms for, statis spherically-symmetric space-times      206—207 214
Ergosphere      316
Ernst equations for axisymmetric space-times with electromagnetic fields      570
Ernst equations for axisymmetric-vacuum space-times      284
Ernst equations for conjugate metrics      285 573
Ernst equations, transformation properties of      285 570
Event horizon(s)      85
Event horizon(s) in an assemblage of black holes      596
Event horizon(s) of Kerr black-hole      313
Event horizon(s) of Reissner — Nordstroem black-hole      214
Event horizon(s) of Schwarzschild black-hole      91
Event horizon(s), flow of electromagnetic energy across      421
Event horizon(s), flow of gravitational energy across      523
Event horizon(s), positivity of energy flow across, for spin-1/2 waves      558
Exterior (or wedge) product      11
Exterior differentiation      12
Gauge freedom      34
Gauge freedom, choice of      68 72 93 140 275 446 566 597—598 620
Gegenbauer functions      144 229 253
Geodesic equation      20 29 30
Geodesic equation as Euler — Lagrange equation      29
Geodesic equation, integrals of      96 97 224 319
Geodesies      20
Geodesies in Kerr space-time, general treatment      342
Geodesies in Kerr space-time, general treatment, $a^{2}>M^{2}$       375
Geodesies in Kerr space-time, general treatment, $a^{2}>M^{2}$ , violation of causality      377
Geodesies in Kerr space-time, general treatment, case of a=M      357
Geodesies in Kerr space-time, general treatment, constants of motion      327 345 367
Geodesies in Kerr space-time, general treatment, equations governing $\theta$ -motion      348 362
Geodesies in Kerr space-time, general treatment, equations governing r-motion      350 363
Geodesies in Kerr space-time, general treatment, exploration of domains of negative r      357
Geodesies in Kerr space-time, general treatment, null geodesies      347
Geodesies in Kerr space-time, general treatment, null geodesies, illustrations of      354—357
Geodesies in Kerr space-time, general treatment, null geodesies, propagation of polarization vector along      358
Geodesies in Kerr space-time, general treatment, principal null-congruences      299—300 349
Geodesies in Kerr space-time, general treatment, time-like geodesies      361
Geodesies in Kerr space-time, general treatment, time-like geodesies, illustrations of      365
Geodesies in Kerr space-time, general treatment, time-like geodesies, marginally bound      365
Geodesies in Kerr space-time, in equatorial plane, $a^{2}>M^{2}$       376

Geodesies in Kerr space-time, in equatorial plane, equations governing      328
Geodesies in Kerr space-time, in equatorial plane, null geodesies, critical orbits      329 341
Geodesies in Kerr space-time, in equatorial plane, null geodesies, illustrations of      332
Geodesies in Kerr space-time, in equatorial plane, time-like geodesies, circular and associated orbits      334 341
Geodesies in Kerr space-time, in equatorial plane, time-like geodesies, illustration of      334
Geodesies in Kerr space-time, in equatorial plane, time-like geodesies, marginally bound      339
Geodesies in Reissner — Nordstroem space-time, null geodesies      216
Geodesies in Reissner — Nordstroem space-time, null geodesies of first and second kind      217
Geodesies in Reissner — Nordstroem space-time, null geodesies, critical orbit      218
Geodesies in Reissner — Nordstroem space-time, null geodesies, illustration of      219
Geodesies in Reissner — Nordstroem space-time, time-like      219
Geodesies in Reissner — Nordstroem space-time, time-like of charged particles      224
Geodesies in Reissner — Nordstroem space-time, time-like of first and second kind      221
Geodesies in Reissner — Nordstroem space-time, time-like, circular orbits, stability of      220
Geodesies in Reissner — Nordstroem space-time, time-like, illustrations of      222 223
Geodesies in Schwarzschild space-time, null geodesies of first kind      130
Geodesies in Schwarzschild space-time, null geodesies of second kind      133
Geodesies in Schwarzschild space-time, null geodesies with imaginary eccentricities      133
Geodesies in Schwarzschild space-time, null geodesies, cone of avoidance      127
Geodesies in Schwarzschild space-time, null geodesies, critical orbits      124
Geodesies in Schwarzschild space-time, null geodesies, illustrations of      128 129
Geodesies in Schwarzschild space-time, null geodesies, radial      123
Geodesies in Schwarzschild space-time, time-like of first kind      103 113
Geodesies in Schwarzschild space-time, time-like of second kind      108 113
Geodesies in Schwarzschild space-time, time-like, bound orbits      100
Geodesies in Schwarzschild space-time, time-like, circular orbits, stability of      106
Geodesies in Schwarzschild space-time, time-like, classification of      101 114
Geodesies in Schwarzschild space-time, time-like, illustrations of      116—21
Geodesies in Schwarzschild space-time, time-like, post-Newtonian approximation to      107
Geodesies in Schwarzschild space-time, time-like, radial      98
Geodesies in Schwarzschild space-time, time-like, unbound orbits      113
Geodesies in Schwarzschild space-time, time-like, with imaginary eccentricities      111 115
Geodesies, affinely parametrized      20 see
Geodesies, Hamiltonians for      96 327
Geodesies, Lagrangians for      96 224 342
Geodesies, time-like, null      33
Geroch — Held — Penrose formalism      64 429
Goldberg — Sachs theorem      62 135 300
Gravitational perturbations      see "Perturbations of Kerr space-time" "Perturbations
Gravitational waves, linearized theory      521 see
Hamilton — Jacobi equation      344
Hawking — Hartle formula      526
Inertial frame      69
Inertial frame, dragging of      70 142 283 289
Initial-value equations      603
Initial-value equations for non-stationary axisymmetric perturbations      604
Initial-value equations for quasi-stationary axisymmetric perturbations      611
Integrability condition (in gravitational perturbations of Kerr space-time)      457 479
Integral identities      487 489 495—496 501
Intrinsic derivative in dyad formalism      538
Intrinsic derivative in tetrad formalism      37
Israel's theorem      299
Jacobi identity      15 26
Jost function      169
Kerr geometry      see also "Kerr metric Kerr
Kerr geometry, electromagnetic waves in      382 see
Kerr geometry, neutrino waves in      546
Kerr geometry, spin-1/2 particles in      531
Kerr metric      289 see
Kerr metric, conjugate of      286
Kerr metric, derivation of      286
Kerr metric, discovery of      302 317
Kerr metric, Hawking — Hartle basis for      423
Kerr metric, its type-D character      300
Kerr metric, its uniqueness      1 292
Kerr metric, Kerr — Schild form      306
Kerr metric, stability of, for axisymmetric perturbations      620
Kerr space-time, additional integrals of geodesic motion in      324
Kerr space-time, description in Newman — Penrose formalism      299
Kerr space-time, gravitational perturbations of      430
Kerr space-time, gravitational perturbations of, systems of equations governing      450—452
Kerr space-time, maximum analytic extension      313
Kerr space-time, nature of      308
Kerr space-time, possible violation of causality      377
Kerr space-time, propagation of electromagnetic waves in Kerr geometry      see "Maxwell's equations in Kerr geometry"
Kerr space-time, ring singularity in      309—10
Kerr space-time, separation of Dirac's equation      544
Kerr space-time, separation of equations governing Weyl scalars      433
Kerr space-time, separation of Hamilton — Jacobi equation      344
Kerr space-time, separation of Maxwell's equations      384
Kerr — Newman metric      see also "Kerr — Newman space-time"
Kerr — Newman metric, conjugate of      574—576
Kerr — Newman metric, derivation of      573
Kerr — Newman metric, discovery of      622
Kerr — Newman metric, its type-D character      579
Kerr — Newman space-time, description in Newman — Penrose formalism      579
Kerr — Newman space-time, perturbations of      580
Kerr — Schild metrics      302
Klein paradox      561
Korteweg-de Vries equation      173 203
Levi — Cevita symbol      68 534
Lie bracket      14 38
Lie derivative      15
Lie derivative, relation to exterior derivative      16
Lie differentiation      14
Lowering indices      27
Lowering indices for spinors      534
Majumdar — Papapetrou solution      591
Maxwell scalars      51
Maxwell scalars for Kerr — Newman space-time      579
Maxwell scalars for Reissner — Nordstroem perturbations      252
Maxwell scalars for Reissner — Nordstroem space-time      226
Maxwell's equations for non-stationary, non-axisymmetric space-times      83
Maxwell's equations for stationary axisymmetric space-times      226
Maxwell's equations for stationary axisymmetric space-times, linearized      227
Maxwell's equations in Kerr geometry      384
Maxwell's equations in Kerr geometry, completion of solution of      392
Maxwell's equations in Kerr geometry, reduction and separation of      385 429
Maxwell's equations in Kerr geometry, solution for vector potential      395
Maxwell's equations in Newman — Penrose formalism      51—52
Maxwell's equations, already linearized for type-D metrics      239
Maxwell's equations, derived from choice of gauge      435
Metric perturbations      see "Perturbations of Kerr space-time" "Perturbations "Perturbations
Metric perturbations of Kerr space-time      430
Metric perturbations of Kerr space-time, expressed in terms of perturbations of basis vectors      445—446
Metric perturbations of Kerr space-time, statement of problem      443
Metric tensor, algebraically special      58 61
Metric tensor, definition      26
Metric tensor, Kerr — Schild form      302
Metric tensor, special forms for      68 72 85 93 205 273 277 302 564 583 588 598
Newman — Penrose formalism      40
Newman — Penrose formalism, null basis for      41
Newman — Penrose formalism, spinorial basis for      538
Non-stationary axisymmetric space-times      70
Non-stationary axisymmetric space-times, reduced form for metric      72 139 598
Non-stationary, non-axisymmetric, space-times, chosen form for metric      73
Non-stationary, non-axisymmetric, space-times, components of Riemann tensor for      78 79
Null congruence      56 see "Principal
Null congruence, conditions for being geodesic      56
Null congruence, conditions for being shear-free      62
Null-tetrad basis      41
Null-tetrad basis for Kerr space-time      299 300
Null-tetrad basis for Kerr — Newman space-time      579
Null-tetrad basis for Reissner — Nordstroem space-time      225
Null-tetrad basis for Schwarzschild space-time      135
Observations, general      1 198 270 427 529 583 596 637
Optical scalars      56 526
Papapetrou transformation      277
Parallel displacement      19
Parity, of perturbations      203 see "Polar
Path length      27
Pauli matrices      536 539 543
Penrose process      366 see
Penrose process, reversible extraction of energy      373
Perihelion, advance of      108
Perturbations of Kerr space-time (in Newman — Penrose formalism)      see also "Integrability condition" "Starobinsky
Perturbations of Kerr space-time (in Newman — Penrose formalism), a last observation      529
Perturbations of Kerr space-time (in Newman — Penrose formalism), choice of gauge      434 443
Perturbations of Kerr space-time (in Newman — Penrose formalism), decoupling and separation of basic equations      433 464 469—70 529
Perturbations of Kerr space-time (in Newman — Penrose formalism), definitions and lemmas      383 432

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