Group Theory and General Relativity

There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups — particularly the Lorentz and the SL(2,C) groups — to the theory of general relativity. Each chapter is concluded with a set of problems.

The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi–Metzner–Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.

The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Contents

• The Rotation Group
• The Lorentz Group
• Spinor Representation of the Lorentz Group
• Principal Series of Representations of SL(2,C)
• Complementary Series of Representations of SL(2,C)
• Complete Series of Representations of SL(2,C)
• Elements of General Relativity Theory
• Spinors in General Relativity
• SL(2,C) Gauge Theory of the Gravitational Field: The Newman-Penrose Equations
• Analysis of the Gravitational Field
• Some Exact Solutions of the Gravitational Field Equations
• The Bondi-Metzner-Sachs Group