A self-contained exposition of general relativity with an emphasis on tetrad and spinor structures and physical measurements on curved manifolds.\ P\ General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be exploited fully without a detailed knowledge of its mathematical structure. This book aims to implement this structure, and then to develop those applications that have been central to the growth of the theory. The first three chapters provide an overview of differential geometry. Chapter 4 extensively analyzes the properties of a tetrad field, subsequently used in Chapter 5 to introduce spinors, in Chapter 8 to describe the geometry of congruences, and in Chapter 9 to define the physical measurements on a curved manifold. The coupling of fields and geometry is investigated in terms of lagrangeans in Chapter 6, and a detailed discussion of some exact solutions of the Einstein equations appears in Chapters 10 and 11.

Geometry and physics: an overview; 1. The background manifold structure; 2. Differentiation; 3. The curvature; 4. Space-time and tetrad formalism; 5. Spinors and the classification of the Weyl tensor; 6. Coupling between fields and geometry; 7. Dynamics on curved manifolds; 8. Geometry of congruences; 9. Physical measurements in space-time; 10. Spherically symmetric solutions; 11. Axially symmetric solutions; References; Notation; Index.