Preface
Summary of Volume I
6 Twistors
6.1 The twistor equation and its solution space
6.2 Some geometrical aspects of twistor algebra
6.3 Twistors and angular momentum
6.4 Symmetric twistors and massless fields
6.5 Conformal Killing vectors, conserved quantities and exact sequences
6.6 Lie derivatives of spinors
6.7 Particle constants; conformally invariant operators
6.8 Curvature and conformai rescaling
6.9 Local twistors
6.10 Massless fields and twistor cohomoiogy
7 Null congruences
7.1 Null congruences and spin-coefficients
7.2 Null congruences and space-time curvature
7.3 Shear-free ray congruences
7.4 SFRs, twistors and ray geometry
8 Classification of curvature tensors
8.1 The null structure of the Weyl spinor
8.2 Representation of the Weyl spinor on S
8.3 Eigenspinors of the Weyl spinor
8.4 The eigenbivectors of the Weyl tensor and its Petrov classification
8.5 Geometry and symmetry of the Weyl curvature
8.6 Curvature covariants
8.7 A classification scheme for general spinors
8.8 Classification of the Ricci spinor
9 Conformal infinity
9.1 Infinity for Minkowski space
9.2 Compactified Minkowski space
9.3 Complexified compactified Minkowski space and twistor geometry
9.4 Twistor four-valuedness and the Grgin index
9.5 Cosmological models and their twistors
9.6 Asymptotically simple space-times
9.7 Peeling properties
9.8 The BMS group and the structure of
9.9 Energy-momentum and angular momentum
9.10 Bondi-Sachs mass loss and positivity
Appendix: spinors in n dimensions
References
Subject and author index
Index of symbols
This is a companion volume to our introductory work Spinors and space-time, Volume 1： two-spinor calculus and relativistic fields. There weattempted to demonstrate something of the power, utility and elegance of2-spinor techniques in the study of space-time structure and physical fields,and to advocate the viewpoint that spinors may lie closer to the heart of (even macroscopic) physical laws than the vectors and tensors of the standard formalism. Here we carry these ideas further and discuss some important new areas of application. We introduce the theory of twistors and show how it sheds light on a number of important physical questions,one of the most noteworthy being the structure of energy-momentum/angular momentum of gravitating systems. The illumination that twistor theory brings to the discussion of such physical problems should lend further support to the viewpoint of an underlying spinorial structure in basic physical laws.
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