## Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time GeometrySpinor 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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### 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 |

465 | |

481 | |

499 | |

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### Common terms and phrases

ABCD apply arise assume asymptotic becomes choice complex complex conjugate components condition conformal conformally invariant congruence consider consists constant construction coordinates corresponding curvature curve defined definition derivative described direction discussion dual effect elements equation example exists expression fact factor field flat follows function geometry given gives holds holomorphic hypersurface identity independent indices infinity integral intersection invariant Killing linear lines massless metric Minkowski momentum multiple namely normal Note null null vector obtain operator original pair particular Penrose physical plane position present projective pure spinors quantities rays referred region relation represented rescaling respectively restricted result rotation satisfies scalar sense simple solutions space space-time spinor standard structure symmetric tangent tensor theory transformations twistor vanishes various vector Weyl zero