Complex General Relativity by Giampiero EspositoComplex General Relativity by Giampiero Esposito

Complex General Relativity

byGiampiero Esposito

Paperback | December 9, 2010

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This volume introduces the application of two-component spinor calculus and fibre-bundle theory to complex general relativity. A review of basic and important topics is presented, such as two-component spinor calculus, conformal gravity, twistor spaces for Minkowski space-time and for curved space-time, Penrose transform for gravitation, the global theory of the Dirac operator in Riemannian four-manifolds, various definitions of twistors in curved space-time and the recent attempt by Penrose to define twistors as spin-3/2 charges in Ricci-flat space-time. Original results include some geometrical properties of complex space-times with nonvanishing torsion, the Dirac operator with locally supersymmetric boundary conditions, the application of spin-lowering and spin-raising operators to elliptic boundary value problems, and the Dirac and Rarita--Schwinger forms of spin-3/2 potentials applied in real Riemannian four-manifolds with boundary. This book is written for students and research workers interested in classical gravity, quantum gravity and geometrical methods in field theory. It can also be recommended as a supplementary graduate textbook.
Title:Complex General RelativityFormat:PaperbackDimensions:218 pagesPublished:December 9, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:904814518X

ISBN - 13:9789048145188

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Table of Contents

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.