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.

Complex General Relativity (Fundamental Theories of Physics) PDF

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