This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research papers, for pedagogical r- sons. Familiarity with fibre-bundle theory is certainly helpful, but in many cases I only rely on two-spinor calculus and conformally invariant concepts in gravitational physics. The key concepts the book is devoted to are complex manifolds, spinor techniques, conformal gravity, ?-planes, ?-surfaces, Penrose transform, complex 3 1 - - space-time models with non-vanishing torsion, spin- fields and spin- potentials. 2 2 Problems have been inserted at the end, to help the reader to check his und- standing of these topics. Thus, I can find at least four reasons for writing yet another book on spinor and twistor methods in general relativity: (i) to write a textbook useful to - ginning graduate students and research workers, where two-component spinor c- culus is the unifying mathematical language.

Inhalt

Preface. Part I: Spinor Form of General Relativity. 1. Introduction to Complex Space-Time. 2. Two-Component Spinor Calculus. 3. Conformal Gravity. Part II: Holomorphic Ideas in General Relativity. 4. Twistor Spaces. 5. Penrose Transform for Gravitation. Part III: Torsion and Supersymmetry. 6. Complex Space-Times with Torsion. 7. Spin-1/2 Fields in Riemannian Geometries. 8. Spin-1/2 Potentials. Part IV: Mathematical Foundations. 9. Underlying Mathematical Structures. Problems for the Reader. Appendix A: Clifford Algebras. Appendix B: Rarita-Schwinger Equations. Appendix C: Fibre Bundles. Appendix D: Sheaf Theory. Bibliography. Subject Index.