Partial Differential Equations in General Relativity

Alan D. Rendall
OXFORD UNIVERSITY PRESS 2008, 296 PAGES PRICE (PAPERBACK) £34.00 ISBN 978-0-19-921541-6
A 20% discount is also available for IMA members

This book is written with two main audiences in mind: physicists with a good knowledge of General Relativity (GR) who wish to gain an understanding of how Partial Differential Equation (PDE theory can be applied to GR; and mathematicians with a good knowledge of PDE theory who want to understand how it is applied to GR. I feel, however that there is a third audience that can profit from the book; academics who have sufficient knowledge in each subject as to be able to find the book accessible but are not specialists in either area of knowledge.

Chapter 1 is a general introduction describing how the book is organised. The next three chapters are concerned with a fairly detailed description of GR, including some applications.

Chapter 5 is a simple, if high-level, description of Ordinary Differential Equations (ODE) as a gentle introduction to the subject of PDEs. Chapter 6 is a good description of Functional Analysis and how it relates to the solution of PDEs; Chapters 7 and 8 describe Elliptic and Hyperbolic PDEs and how they relate to GR.

From Chapter 9 onwards the content is aimed at both physicists and mathematicians as the two aspects of the book, GR and PDE are developed together, so that GR is investigated using PDE knowledge.

This book is clearly most suitable for people whose background in either of GR or PDE, or both, is quite advanced. Some of the topics discussed, even in Chapter 6, I have seen only in the series of books ‘Partial Differential Equations’ volumes 1-3 by Professor Taylor. The book can most profitably be read by postgraduates particularly those working at PhD level or higher.