Penrose R., Rindler W. — Spinors and space-time. Spinor and twistor methods in space-time geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Penrose R., Rindler W. — Spinors and space-time. Spinor and twistor methods in space-time geometry

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Название: Spinors and space-time. Spinor and twistor methods in space-time geometry

Авторы: Penrose R., Rindler W.

Аннотация:

Spinor and Twistor Methods in Space-Time Geometry introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Repr

Год издания: 1988

Количество страниц: 512

Добавлена в каталог: 26.03.2011

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Предметный указатель

Orientable, space- and time-      3
Orthochronous      15
Orthogonal group      see "Rotation group"
Outer product of twistors      50 51
P      27 31
P ( $\rho, \sigma$ matrix)      183
Parabolic section of null cone      (301) 378
Parker, T.      430
Partial derivatives in abstract-index formalism      141
Particle, massive      70 74
Particle, massless      68
Past-      see "Future-"
Patodi, V.K.      434
Pauli — Lubanski spin vector      69 420
Payne, W.T.      3 8
Pedoe, D.      452
Peeling property      358
Peeling property for gravitational field      364
Pencil of hyperplanes      337 343
Pencil, plane (of lines)      311 312
Penrose diagram for GPND specialization      226 256
Penrose diagram, conformal diagram      293 334
Penrose, R.      (29) 44 45 60 66 68 71 (74) 78 79 81 91 (103) 107 108 110 126 129 131 (139) 145 148 (149) 164 180 (184) 185 197 (206) (207) 211 213 215 216 217 223 227 230 231 264 265 275 (283) 285 296 297 298 (302) 303 (308) (310) 325 326 335 338 350 351 353 354 358 359 364 369 388 389 390 (391) 392 394 395 (396) 421 422 423 (424) 426 427 428
Perfect fluid      290 347
Perjes, Z.      (74) 148
Perry, M.J.      424 430 431 434
Petrov canonical forms      245 246
Petrov classification      223 225 242
Petrov types      225
Petrov types and Jordan forms      240
Petrov, A.Z.      223 246
Phase rotation of a twistor      69
Pin groups      (440)
Pirani, F.A.E.      211 223 227 (407)
Plane (2-plane) in PT      312
Plane (2-plane), totally null      64 309 see beta-plane"
Plane pencil      311 312
Plebahski spinor type      265 285
Plebanski, J.      (199) 265 285 (310) see
Pluecker, J.      (308)
PND (principal null direction)      13
PND (principal null direction) and $\mathbb{C}\mathbb{S}^{+}$       267
PND (principal null direction) for complex space-time      129
PND (principal null direction) of angular momentum      70
PND (principal null direction) of Lorentz transformation      15
PND (principal null direction) of Weyl spinor      107 184 190 223 see
PND (principal null direction), k-fold      13 190
PND (principal null direction), k-fold and pole-multiplicity of twistor functions      204
PNDs of (EPNDs), electromagnetic (Maxwell) field tensor      198 255 257 259 264 331
PNDs of gravitational field      223 see
PNDs of Weyl (conformal) tensor, spinor      223 see
Poincare group      67 84 304 366
Poincare group as subgroup of BMS group      380
Poincare group as subgroup of BMS group and gravitational radiation      390
Poincare group as subgroup of complex BMS group      423
Poincare group as subgroup of NU group      369
Poincare lemma (converse)      16 90 438
Point of Minkowski space, in twistor terms      63 65
Point of Minkowski space, in twistor terms, complex      66 149
Point of space-time, in twistor terms      63 65 305
Point of space-time, in twistor terms, complex      66 128 307
Polytrope      347
Porrill, J.      368
Porteous, I.R.      (440) 441 452
Porter, J.      44
Position vector      45 127
Position vector, complex      66 151
Position vector, complex conjugate of      66
Positive frequency      37 152 316
Positive frequency of twistor wave function      145 151
Poston, T.      136
Potential      see also "Gauge freedom"
Potential for angular momentum twistor      71
Potential for Killing vector      88
Potential for linear gravity      38
Potential for massless fields      78
Potential for Maxwell theory      32
Potential for Yang — Mills theory      35
Potential, Hertz-type      81
Press, W.H.      350 428
Primary spinor part of twistor      52
Primary spinor part of twistor of symmetric trace-free twistor      54 75 82 94 96 101 118 119 147
Primary spinor part of twistor, does it determine the twistor?      53
Priming operation      19 24 (197)
Principal null directions      13 see
Principal null vectors      13
Principal spinors      13
Prior, C.R.      421
Projection operator      26 443
Projection part of twistor      52
Projection part of twistor, 2-surface      403 413 414 432
Projection part of two-surface twistor      403 414 432
Projective line      149 307
Projective space      248 267 300 337 452 453
Projective twistor space      56 (57) 149 307
Proof of peeling property      363 364
Propagation of connecting vector      175
Proper      15
Pseudo-orthogonal group      440 see
Pure spinors (N-dimensional)      451
Purely electric      33 257 258
Purely electric, shear of cut      389 412 421
Q (particle constant)      105
Qadir, A.      (149)
Quadric      267 301 452 453 456
Quadruple point      286 290
Quadrupole moment      425 428
Quantization      142
Quantum chromodynamics      461
Quantum commutator      142
Quantum commutator, twistor      143
Quasi-local energy-momentum/angular momentum expression      401 see
Quasi-local energy-momentum/angular momentum expression and ADM mass      404
Quasi-local energy-momentum/angular momentum expression at $\mathscr{I}$       408
Quasi-local energy-momentum/angular momentum expression in Schwarzschild space      405 407 408
Quasi-local energy-momentum/angular momentum expression in time-symmetric space      405
Quasi-local energy-momentum/angular momentum expression, quasi-local angular momentum twistor      402 (406)
Quasi-local energy-momentum/angular momentum expression, Tod form      (401) 405 432
Quasi-local mass in FRW (Friedmann — Robertson — Walker) models      407
Quasi-local mass in Reissner — Nordstrom space-time      406 407
Quasi-local mass in Schwarzschild space-time      405 407 408
R (projective line in $\mathbb{PT}^{\bullet}$ )      149
R(U) universe radius      332
Radiation field      359 364 388
Radiation field, ill-defined at spacelike $\mathscr{I}$       365
Radiation fields are null massless fields      359
Rarita — Schwinger equation      see "Dirac — Fierz equation"
Ray (null geodesic)      58 169
Ray congruence      169 see
Ray congruence, hypersurface orthogonal      179
Ray congruence, twist-free      179 207
Real curve on $S^{+}$ (anti-celestial sphere)      266 274
Real part of complex curve on $CS^{+}$       274
Reality of point of Minkowski space, in twistor terms      66 67
Reality of point of space-time, in twistor terms      66 67 313
Reality structure of $\mathbb{C}\mathbb{M}^{*}$       313
Reality structure of N-dimensional spinors      459 460
Reasonableness of asymptotic simplicity      347 350 366
Reasonableness of infinity (conformal)      347 350 366
Reduced (N-dimensional) spinors      66 443
Reducibility (curve)      266 276 277 286
Reducibility of complex curve on $CS^{+}$       266 276
Reducibility of symmetric spinor      266
Reissner — Nordstrom space-time      198
Representation theory for BMS (Bondi — Metzner — Sachs) group      (380)
Resolution      118
Resolution of exact sequences      118
Resolution of massless free field      116
Resolution of twistor equation      118 119
Rest mass      see also "Mass" "Massless

Rest mass for many-twistor system      74
Rest mass, quantized      144
Rest mass, quasi-local      404 (406)
Restricted Minkowski coordinates      1
Restricted Minkowski tetrad      6 7
Restriction in covering      159
Restriction of complex structure      212
Retarded time coordinate      292 348 356
Retarded time coordinate, Bondi      373 380 393
Reula — Tod mass-positivity proof      434
Reula, O.      424 430 434
Ricci identities      15
Ricci spinor (trace-free Ricci tensor)      20
Ricci spinor (trace-free Ricci tensor) classification      223 265 275 282
Ricci spinor (trace-free Ricci tensor), conformally rescaled      121
Ricci tensor      20 121 265 275 352
Riemann curvature tensor      19 20
Riemann principal directions      247
Riemann principal directions of Weyl (conformal) tensor, spinor      247
Riemann sphere      1 149 153 292
Riemann theorem (on conformal $S^{2}$ )      355
Right-      see "Left-"
Rindler, W.      177 332 335 336 337
Robertson — Walker models      332 see
Robinson congruence      59 70 72 189 203 204 299 300 314 318 322
Robinson congruence, special      63
Robinson — Trautman metrics      350
Robinson's theorem      191 205 206 222
Robinson, I.      126 173 191 192 195 198 (199) 350
Role of analyticity (real-analytic) in Kerr theorem      221 222
Role of analyticity (real-analytic) in Robinson theorem      222
Ross, N.F.      187 188
Rossi, H.      161
Rotation group in n-dimensions      440
Rotation group in six dimensions (pseudo-)      66 303
Rotation group, complex      (233)
Rotation of ray congruence      177 see
Rotation rate of Robinson congruence      323 324
Rotations      2 see
Rotations of metric sphere      29
ROTENBERG, M.A.      (396) 427
Round sphere      see "Metric sphere"
Rudiger, R.      110
s = n - 2u (signature of n-dimensional $g_{ab}$ )      443
Sachs equations      183
Sachs equations and fingerprints      230 (231)
Sachs peeling property      358 see
Sachs, R.K.      77 179 183 185 191 195 350 358 359 (380) 382 388 (391) (396) 415 423 (424)
Scalar curvature at infinity (conformal)      374 376
Scalar product of twistors      49
Scalars of electromagnetic (Maxwell) field tensor      257
Scalars of Weyl (conformal) tensor, spinor      235
Scanlan, G.      265 277
Scheffers, G.      (210) (308)
Schild, A.      195 198 (199)
Schoen, R.      424 429
Schouten, J.A.      127 (214)
Schroedinger — Klein — Gordon equation      40
Schroedinger, E.      337
Schwarzschild space-time      108 205 229 231 331 332 347
Scri ( $\mathscr{I}$ )      291 see
Second fundamental form      see "Extrinsic curvature"
Segre characteristic      285
Seifert, H.-J.      297
Self-dual      12 242 419 452
Self-dual Weyl curvature      21 129 164 390
Self-dual Yang — Mills curvature      35 164
Sen — Witten (SW-) equation      430
Sen, A.      430 431
SFR (shear-free ray congruence)      189 see
SFR (shear-free ray congruence), behaviour of $\rho$ in Einstein space      189
Shanahan, P.      399 454
Shaw, W.T.      404 423 433 461
Sheaf      117 (160)
Shear of ray congruence      171 177 178
Shear structure of      384
Shear structure of and gravitational radiation      388
Shear-free property of Robinson congruence      60
Shear-freeness      60 189 212 216 see
Shear-freeness at $\mathscr{I}$       385
Shear-freeness at hypersurface      219
Shear-freeness of $\mathscr{I}$       355
Signature      43 (64) 67 128 (129) 303 306 403 411 440 443 459 462
Simple skew tensors      14 247 451 452
Simple skew tensors, Maxwell field      33 257
Singer, I.M.      44 (129) 390 434
Singer, M.A.      (124)
Singularities of complex curve      269
Singularity at $i^{\pm}, i^{0}$       349
Singularity of fingerprint      (232)
Singularity of space-time (naked)      204
Singularity of twistor function      114 148 204
Skew symmetry      see "Anti-symmetric"
SL(2, $\mathbb{C}$ ) (spin group)      10
SO(n), SO(p, q), Spin(n), Spin(p, q)      440
Sommerfeld radiation condition      365
Sommerfeld, A.      365
Sommers, P.D.      108 (109) 110 126 191 193 194 195 461
Space of ray      207
Space-time complex      127
Space-time, manifold      210
Spacelike 2-surface      26
Sparling's 3-form      437
Sparling, G.A.J.      (74) 78 148 (149) (217) 437 462
Specialization scheme for Ricci spinor (trace-free Ricci tensor)      287
Spherical harmonics (spin-weighted)      29 383 410 427 428
Spherical harmonics (spin-weighted), table of dimensions      30
Spin      69 70 204 see
Spin and fingerprints      (231) (232)
Spin group      2 10 (233)
Spin group, N-dimensional      440
Spin raising and lowering      75 79 80 147
Spin structure, spinor structure      3
Spin structure, spinor structure of $\mathbb{M}^{#}$       318
Spin structure, spinor structure of $\mathbb{M}^{#}$ , behaviour under reflections      321 322
Spin structure, spinor structure of $\mathbb{M}^{#}$ , twisted      324
Spin transformation      2 14 15
Spin-coefficient formalism      17 169 see
Spin-coefficients      17
Spin-coefficients, $\rho, \sigma$ and $\tau$ in flat space      185
Spin-coefficients, change under basis change      23 171 173 177
Spin-coefficients, change under conformal rescaling      36
Spin-coefficients, interpreting $\kappa$       170
Spin-coefficients, interpreting $\rho, \sigma$       173 178
Spin-coefficients, interpreting $\tau$       175 177
Spin-coefficients, interpreting $\varepsilon$       172
Spin-coefficients, type      23 171 173 174
Spin-frame      6 18
Spin-frame, behaviour at $\mathscr{I}$       362 363
Spin-matrix      2
Spin-space      3
Spin-space, N-dimensional      441
Spin-space, N-dimensional, reduced      443
Spin-vector      2 3 8 101 170
Spin-vector bundle      3 437
Spin-weight      23 29 440
Spin-weight and fingerprints      233
Spin-weighted spherical harmonics      29 383 410 427 428
Spin-weighted spherical harmonics, table of dimensions      30
Spinor basis      6
Spinor fields      4
Spinor fields, N-dimensional      462
Spinor form of Ricci identities      21 22
Spinor form of Ricci identities, Yang — Mills      35
Spinor parts of dual twistor      50
Spinor parts of dual twistors      50
Spinor parts of higher-valent twistors      51
Spinor parts of twistors      47 51 see
Spinor parts of twistors, dependence on position      46 49 53
Spinor-tensor correspondence      5

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