Relativity on Curved Manifolds

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurement on curved manifolds.

F. de Felice (Author), C. J. S. Clarke (Author)

9780521266390, Cambridge University Press

Hardback, published 25 May 1990

464 pages
23.6 x 15.9 x 3.5 cm, 0.87 kg

' … a useful book with some unusual features which will win it a place on relativists' shelves and may be of interest to mathematical physicists in general.' Contemporary Physics

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.

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.

Subject Areas: Relativity physics [PHR]