Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry

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Cambridge University Press, Apr 7, 1988 - Science - 512 pages
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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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The spinors is space independent. If transformation to anothe form, it might got another form of the Dirac-equation

Contents

Twisters
43
62 Some geometrical aspects of twistor algebra
58
63 Twistors and angular momentum
68
64 Symmetric twistors and massless fields
75
65 Conformal Killing vectors conserved quantities and exact sequences
82
66 Lie derivatives of spinors
101
67 Particle constants conformally invariant operators
104
68 Curvature and conformal reseating
120
86 Curvature covenants
258
87 A classification scheme for general spinors
265
88 Classification of the Ricci spinor
275
Conformal infinity
291
92 Compactified Minkowski space
297
93 Complexified compactified Minkowski space and twistor geometry
305
94 Twistor fourvaluedness and the Grgin index
316
95 Cosmological models and their twistors
332

69 Local twistors
127
610 Massless Fields and twistor cohomology
139
Null congruences
169
72 Null congruences and spacetime curvature
182
73 Shearfree ray congruences
189
74 SFRs twistors and ray geometry
199
Classification of curvature tensors
223
82 Representation of the Weyl spinor on S
226
83 Eigenspinors of the Weyl spinor
233
84 The eigenbivectors of the Weyl tensor and its Petrov classification
242
85 Geometry and symmetry of the Weyl curvature
246
96 Asymptotically simple spacetimes
347
97 Peeling properties
358
98 The BMS group and the structure of G
366
99 Energymomentum and angular momentum
395
910 BondiSachs mass loss and posit ivity
423
spinors in n dimensions
440
References
465
Subject and author index
481
Index of symbols
499
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