C. J. S. Clarke - Böcker

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurements on curved manifolds. General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be fully explained without a detailed knowledge of its mathematical structure. The aim of this book is to introduce this structure, and then to use it to develop those applications that have been central to the growth of the theory. An overview of differential geometry is provided and properties of a tetrad field are then extensively analysed. These are used to introduce spinors, to describe the geometry of congruences and define the physical measurements on a curved manifold. The coupling of fields and geometry is investigated in terms of Lagrangeans and a detailed discussion of some exact solutions of the Einstein equations are provided.

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurements on curved manifolds. General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be fully explained without a detailed knowledge of its mathematical structure. The aim of this book is to introduce this structure, and then to use it to develop those applications that have been central to the growth of the theory. An overview of differential geometry is provided and properties of a tetrad field are then extensively analysed. These are used to introduce spinors, to describe the geometry of congruences and define the physical measurements on a curved manifold. The coupling of fields and geometry is investigated in terms of Lagrangeans and a detailed discussion of some exact solutions of the Einstein equations are provided.

The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While the Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.