## 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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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 |

465 | |

481 | |

499 | |

### Common terms and phrases

2-surface a-plane ABCD algebra angular momentum apply asymptotic Bondi choice complex conjugate components condition conformal geometry conformal rescaling conformal weight conformally flat conformally invariant consider constant coordinates corresponding curvature curve defined derivative discussion dual eigenspinors eigenvalues eigenvectors expression fact factor field equations flag plane flagpole follows functions geometry given GPNDs gravitational Grgin Hermitian holomorphic hyperplane hypersurface independent indices infinity integral intersection light cone linear Lorentz manifold massless field matrix metric Minkowski space multiple non-zero notation Note null directions null hypersurface obtain orthogonal Penrose PNDs Poincare pure spinors quantities rays referred relation represented respectively restricted rotation satisfies scalar sequence simple skew solutions space-time spacelike spin-frame spin-space spin-weight spinor fields symmetric tangent tensor theorem timelike trace-free transformations twistor equation twistor space twistor theory unprimed vanishes vector space Weyl spinor Weyl tensor zero