Perturbations of Kerr space-time (in Newman — Penrose formalism), equations already linearized 431 432
Perturbations of Kerr space-time (in Newman — Penrose formalism), integral identities derived from 487 489 495—496 501
Perturbations of Kerr space-time (in Newman — Penrose formalism), retrospect 497
Perturbations of Kerr space-time (in Newman — Penrose formalism), systems of equations governing 450—452
Perturbations of Reissner — Nordstroem space-time see also "Axial perturbations" "Polar
Perturbations of Reissner — Nordstroem space-time, equations governing 228 233 242
Perturbations of Reissner — Nordstroem space-time, reduction to one-dimensional wave-equations 230 234
Perturbations of Reissner — Nordstroem space-time, via metric perturbations 228
Perturbations of Reissner — Nordstroem space-time, via Newman — Penrose formalism 238
Perturbations of Reissner — Nordstroem space-time, via Newman — Penrose formalism, decoupling of equations 243
Perturbations of Schwarzschild space-time 139 see "Polar
Perturbations of Schwarzschild space-time, considered as a limit of Kerr space-time 500
Perturbations of Schwarzschild space-time, equations governing 143 148 176
Perturbations of Schwarzschild space-time, reduction to one-dimensional wave-equations 144 150
Perturbations of Schwarzschild space-time, via metric perturbations 142
Perturbations of Schwarzschild space-time, via Newman — Penrose formalism 174
Petrov classification 58
Petrov classification, conditions for different types 61—62
Petrov type-D space-times see "Type-D space-times"
Phantom gauge 180 241
Phantom gauge, appropriateness for Kerr — Newman perturbations 582
Phantom gauge, leading to Maxwell's equations 435
Poincare's lemma 12
Polar perturbations 142
Polar perturbations for Reissner — Nordstroem space-time 230
Polar perturbations for Reissner — Nordstroem space-time, particular integral for 235
Polar perturbations for Schwarzschild space-time 145
Polar perturbations for Schwarzschild space-time, particular integral for 159
Polar perturbations for Schwarzschild space-time, particular integral for, theorem relating to 152
Polar perturbations, expression in terms of axial perturbations 162 237
Potential barriers for Kerr black-hole, for incident Dirac-waves 555
Potential barriers for Kerr black-hole, for incident electromagnetic-waves 404
Potential barriers for Kerr black-hole, for incident gravitational-waves 507
Potential barriers for Kerr black-hole, for incident neutrino-waves 548
Potential barriers for Reissner — Nordstroem black-hole, for axial perturbations 236—237
Potential barriers for Reissner — Nordstroem black-hole, for polar perturbations 236—237
Potential barriers for Schwarzschild black-hole, for axial perturbations 145 146
Potential barriers for Schwarzschild black-hole, for polar perturbations 150 151
Potential barriers, complex 405 507
Potential barriers, their common form 160 187 199 236 270 505
Potential scattering, the theory of 166
Potential scattering, the theory of, application to Reissner — Nordstroem black-hole 267
Principal null-congruences 59
Principal null-congruences in Kerr space-time 299 349
Principal null-congruences in Reissner — Nordstroem space-time 216
Principal null-congruences in Schwarzschild space-time 124 135
Problem of reflexion and transmission by complex potential-barriers 410 514
Problem of reflexion and transmission for Kerr black-hole, for incident Dirac-waves 556
Problem of reflexion and transmission for Kerr black-hole, for incident electromagnetic-waves 410
Problem of reflexion and transmission for Kerr black-hole, for incident gravitational-waves 514
Problem of reflexion and transmission for Kerr black-hole, for incident neutrino-waves 548
Problem of reflexion and transmission for Reissner — Nordstroem black-hole 254
Problem of reflexion and transmission for Schwarzschild black-hole 163 193
Quasi-normal modes of Kerr black-hole 528
Quasi-normal modes of Reissner — Nordstroem black-hole 261
Quasi-normal modes of Schwarzschild black-hole 201
Raising indices 27
Raising indices for spinors 534
Reflexion amplitude 164
Reflexion amplitude, difference of phase, for axial and polar perturbations 166 254
Reflexion and transmission coefficients 164
Reflexion and transmission coefficients for Kerr black-hole 514
Reflexion and transmission coefficients for Kerr black-hole, equality of, for four allowed potential barriers 515
Reflexion and transmission coefficients for Kerr black-hole, for incident electromagnetic-waves 416
Reflexion and transmission coefficients for Kerr black-hole, for incident electromagnetic-waves, expressed in terms of Maxwell scalars and Teukolsky functions 418—19
Reflexion and transmission coefficients for Kerr black-hole, for incident gravitational-waves 519
Reflexion and transmission coefficients for Kerr black-hole, for incident gravitational-waves, expressed in terms of Weyl scalars and Teukolsky functions 517—19
Reflexion and transmission coefficients for Kerr black-hole, for incident neutrino-waves 550
Reflexion and transmission coefficients for Reissner — Nordstroem black-hole 255 258
Reflexion and transmission coefficients for Reissner — Nordstroem black-hole, expressed in terms of Weyl and Maxwell scalars 256
Reflexion and transmission coefficients for Schwarzschild black-hole 165
Reflexion and transmission coefficients for Schwarzschild black-hole, expressed in terms of Weyl scalars 196—198
Reflexion and transmission coefficients, equality of, for axial and polar perturbations 164 254
Reflexion and transmission coefficients, integral equations for 170
Regge — Wheeler equation 144
Reissner — Nordstroem black-hole see also "Reissner — Nordstroem space-time" "Cauchy
Reissner — Nordstroem black-hole an assemblage of, extreme 593
Reissner — Nordstroem black-hole, quasi-normal modes 262
Reissner — Nordstroem black-hole, stability of 262
Reissner — Nordstroem metric, derivation of 205 214
Reissner — Nordstroem space-time, description in Newman — Penrose formalism 224
Reissner — Nordstroem space-time, geodesies see "Geodesies"
Reissner — Nordstroem space-time, maximum analytic extension 212
Reissner — Nordstroem space-time, nature of 209
Reissner — Nordstroem space-time, perturbations of 226
Reissner — Nordstroem space-time, perturbations of, via metric perturbations 226
Reissner — Nordstroem space-time, perturbations of, via Newman — Penrose formalism 238
Reissner — Nordstroem space-time, stability of 262
Relativistic anomaly 104
Retrospect 497
Ricci identities in Newman — Penrose formalism 46—47
Ricci identities, eliminant relations, derived from 47—48
Ricci identities, expressed in terms of rotation coefficients in a tetrad basis 39
Ricci identities, linearized 470
Ricci identity 24 33
Ricci identity in tetrad formalism 39
Ricci rotation-coefficients see "Rotation coefficients"
Ricci tensor 25 31
Ricci tensor in Newman — Penrose formalism 42
Ricci tensor, components of, for non-stationary axisymmetric space-times 141
Ricci tensor, components of, for stationary axisymmetric space-times 274 601 602
Riemann tensor in Newman — Penrose formalism 42
Riemann tensor, components of, for Kerr space-time 291—292
Riemann tensor, components of, for Majumdar — Papapetrou metric 589
Riemann tensor, components of, for non-stationary axisymmetric space-times (in a general gauge) 599—601
Riemann tensor, components of, for non-stationary, non-axisymmetric space-times 78 79
Riemann tensor, components of, for Reissner — Nordstroem space-time 215
Riemann tensor, components of, for Schwarzschild space-time 95
Riemann tensor, components of, for static spherically-symmetric space-times 86 87
Riemann tensor, components of, for stationary axisymmetric space-times 274
Riemann tensor, definition 23
Riemann tensor, symmetries of 30
Riemann tensor, tetrad components of 37
Riemannian geometry 28
Robinson's lemmas 294
Robinson's theorem 292
Rotation coefficients 37
Rotation coefficients, antisymmetry of 37
Rotation coefficients, as spin coefficients 42
Rotation coefficients, explicit expressions for 82 300
Rotations, of bases 180 240 423 434 581
Rotations, of bases, of classes one, two, and three 53
Scalar product 29
| Scattering (S) matrix 168
Scattering (S) matrix for Reissner — Nordstroem black-hole 260
Scattering (S) matrix, unitarity of 168
Scattering (S) matrix, unitarity of, for Kerr black-hole 419 520
Scattering (S) matrix, unitarity of, for Reissner — Nordstroem black-hole 260
Scattering (S) matrix, unitarity of, for Schwarzschild black-hole 197
Schrodinger wave-equation see "Wave equations one-dimensional"
Schwarzschild black-hole see also "Schwarzschild space-time"
Schwarzschild black-hole, quasi-normal modes of 201
Schwarzschild black-hole, stability of 199
Schwarzschild metric, derivation of 85 93
Schwarzschild metric, discovery of 136
Schwarzschild space-time 86
Schwarzschild space-time, description in Kruskal frame 90
Schwarzschild space-time, description in Newman — Penrose formalism 134
Schwarzschild space-time, geodesies (time-like) in 96 see
Schwarzschild space-time, nature of 90
Schwarzschild space-time, perturbations of 139 see
Self adjoint 615 621
Separation of variables 144 147 229 231 344 386 433 464 545
Singularity in Kerr space-time 309
Singularity in Reissner — Nordstroem space-time 214
Singularity in Schwarzschild space-time 92 95
Singularity, naked 375
Space-times, non-stationary axisymmetric 71
Space-times, non-stationary, non-axisymmetric 73
Space-times, spherically symmetric 85
Space-times, static axisymmetric 583
Space-times, stationary axisymmetric 66
Spin coefficients 540
Spin coefficients for Kerr space-time 300
Spin coefficients for Reissner — Nordstroem space-time 225
Spin coefficients for Schwarzschild space-time 135 175
Spin coefficients, expressed in terms of rotation coefficients 42
Spin coefficients, spinorial definition 540
Spin coefficients, spinorial definition, symmetry of 541
Spinor analysis 531
Spinors as a flag 537
Spinors definition 533
Spinors, Dirac's lectures on 561
Spinors, see-saw 535
Starobinsky constant as it occurs in transformation theory 408 506
Starobinsky constant for spin-1 fields 388 391
Starobinsky constant for spin-2 fields 437 440
Starobinsky constant for spin-2 fields, real and imaginary parts of 463
Static axisymmetric space-times 583 see
Static black-holes see also "Distorted black-holes" "Reissner "Schwarzschild
Static black-holes an assemblage of 592
Static black-holes, general observations on 198 270
Stationary axisymmetric space-times, basic equations for 274—275 280
Stationary axisymmetric space-times, choice of gauge 278 566 584
Stationary axisymmetric space-times, chosen form for metric 68
Stationary axisymmetric space-times, conjugate metrics 276 572
Stationary axisymmetric space-times, dragging of inertial frame 69
Stationary axisymmetric space-times, Riemann tensor for 274
Stationary axisymmetric space-times, X and Y functions 280 283
Structure constants 38
Structure constants for Kerr space-time 449
Structure constants in Newman — Penrose formalism 45
Structure constants in tetrad formalism 39
Super radiance, in Kerr space-time see also "Hawking — Hartle formula"
Super radiance, in Kerr space-time, absence of, for incident Dirac-waves 558
Super radiance, in Kerr space-time, absence of, for incident neutrino-waves 550
Super radiance, in Kerr space-time, condition for occurrence of 400 415 425
Super radiance, in Kerr space-time, for incident electromagnetic-waves 415 419 425
Super radiance, in Kerr space-time, for incident gravitational-waves 517 520
Tetrad components 36
Tetrad components, relation to tensor components 36
Tetrad formalism 34 81
Tetrad frame for axisymmetric space-times 69
Tetrad frame for non-statonary space-times 81
Tetrad frame, freedom in choice of 53 240 446 581
Tetrad transformations 53 180 240 423 434 581
Tetrad transformations to Hawking — Hartle basis 423 525
Teukolsky equations for spin-1 fields 386
Teukolsky equations for spin-2 fields 434
Teukolsky equations, transformation of 397
Teukolsky functions, integral identities for 487 495—497 501
Teukolsky functions, relative normalization of, s=1 392
Teukolsky functions, relative normalization of, s=2 458
Teukolsky functions, tables of 626—34
Teukolsky — Starobinsky identities for spin-1 fields 386
Teukolsky — Starobinsky identities for spin-2 fields 436
Torsion 21
Torsion tensor 19 22
Transformation theory for Kerr perturbations 502
Transformation theory for Reissner — Nordstroem perturbations 245
Transformation theory for Schwarzschild perturbations 182
Transformation theory for Teukolsky equations 400
Transmission amplitude(s) 164
Transmission amplitude(s), condition for equality of 173
Transmission amplitude(s), equality of, for axial and polar perturbations 164 254
Transmission amplitude(s), series expansion for 171
Type-D space-times 59
Type-D space-times, complex integral for null-geodesic motion in 320
Type-D space-times, conditions for 61—63
Type-D space-times, conditions for, satisfied by Kerr metric 300
Type-D space-times, conditions for, satisfied by Reissner — Nordstroem metric 225
Type-D space-times, conditions for, satisfied by Schwarzschild metric 135
Type-D space-times, integral for geodesic motion in 322
Variational methods for treatment of axisymmetric space-times 614
Variational Principle 619
Wald inequality 370
Walker — Penrose theorem 320
Wave equations, one-dimensional 144 150 230 235 400 503 see
Wave equations, one-dimensional, theorem relating to 161
Weyl scalar,  , equations governing, for type-D space-times 319
Weyl scalar, , for Kerr space-time 302
Weyl scalar, , for Kerr — Newman space-time 580
Weyl scalar, , for Reissner — Nordstroem space-time 225
Weyl scalar, , for Schwarzschild space-time 136
Weyl scalars 43
Weyl scalars for Kerr perturbations 431 518—20
Weyl scalars for Reissner — Nordstroem perturbations 249
Weyl scalars for Schwarzschild perturbations 188
Weyl scalars, flux of gravitational energy expressed in terms of 522
Weyl tensor 31
Weyl tensor, expressed in terms of Weyl scalars 44
Weyl's solutions 623
wronskian 164 167 194 403 552 557
X and Y functions (for axisymmetric space-times) 280
X and Y functions (for axisymmetric space-times), transformation properties of 281
Zerilli equation 150
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