The Wave Equation on a Curved Space-Time

This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves.

F. G. Friedlander (Author)

9780521136365, Cambridge University Press

Paperback, published 25 February 2010

296 pages
22.9 x 15.2 x 1.7 cm, 0.44 kg

This book was originally published in 1975. In Einstein's General Theory of Relativity the effects of gravitation are represented by the curvature of space-time. Physical processes occurring in the presence of gravitation must then be treated mathematically in terms of their behaviour in a curved space-time. One of the most basic of these processes is wave propagation, and this book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role. Although much of the book deals with four-dimensional space-time, the n-dimensional case is also treated, more briefly. The subject-matter is also of interest in other branches of mathematical physics and, as a fresh account of the classical work of Hadamard and M. Riesz, in the theory of partial differential equations.

Preface
1. Differential geometry
2. Distribution theory
3. Characteristics and the propagation of discontinuities
4. Fundamental solutions
5. Representation theorems
6. Wave equations on n-dimensional space-times
Appendix
Bibliography
Notation
Index.

Subject Areas: Physics [PH]