Complex General Relativity

1. Front Matter

   Pages i-xii

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2. Spinor form of General Relativity

   1. Front Matter

      Pages 1-1

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   2. Introduction to Complex Space-Time

      Pages 2-16

   3. Two-Component Spinor Calculus

      Pages 17-29

   4. Conformal Gravity

      Pages 30-41

3. Holomorphic Ideas in General Relativity

   1. Front Matter

      Pages 42-42

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   2. Twistor spaces

      Pages 43-60

   3. Penrose Transform for Gravitation

      Pages 61-77

4. Torsion and Supersymmetry

   1. Front Matter

      Pages 78-78

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   2. Complex Space-Times with Torsion

      Pages 79-92

   3. Spin-1/2 Fields in Riemannian Geometries

      Pages 93-110

   4. Spin-3/2 Potentials

      Pages 111-135

5. Mathematical Foundations

   1. Front Matter

      Pages 136-136

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   2. Underlying Mathematical Structures

      Pages 137-168

6. Back Matter

   Pages 169-205

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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.

• Boundary value problem
• Gravity
• Minkowski space
• Potential
• RMS
• Relativity
• general relativity
• partial differential equations

• National Institute for Nuclear Physics, Naples, Italy

  Giampiero Esposito

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