Complex General Relativity - Esposito, Giampiero

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Résumé :
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.

Biographie:
Prof. Giampiero Esposito (1962) obtained an honours (cum laude) degree in Physics from Naples University in 1986, and was a St. John's Benefactor's Scholar at DAMTP in Cambridge (UK) from 1987 to 1991, where he received the J.T. Knight Prize Essay award in 1989 and obtained his Ph.D. degree. He was elected to INFN and ICTP post-doctoral positions at Naples and Trieste, respectively, and has been an INFN Research Fellow at Naples (position with tenure) since 1993, and INFN Primo Ricercatore since 2007. His original contributions are mainly devoted to quantum gravity and quantum field theory on manifolds with boundary (one-loop conformal anomalies, mixed and diff-invariant boundary conditions for Euclidean quantum gravity, heat-kernel asymptotics, Casimir effect and measurement of variations of zero-point energy), spontaneous symmetry breaking in the early universe, accelerated expansion of the universe, singularity avoidance in quantum cosmology, and scattering fromsingular potentials in quantum mechanics....

Sommaire:
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.