Conformal Methods in General Relativity

Conformal methods in general relativity is the first comprehensive text which covers this topic of mathematical relativity. The conformal method is based on the idea of introducing a conformal (angle preserving) transformation of the metric and reformulating the gravitational field equation, one arrives at what are called the conformal Einstein field equations. When this formulation is combined with the modern theory of partial differential equations, one arrives at a powerful method which allows one to study global properties of solutions of the Einstein field equations. The book is a self-contained exposition of this subject and should be accessible to readers with some General Relativity background. Part I of the book introducing the necessary geometrical tools which are beyond the introductory level textbook material while Part II discusses General Relativity in this conformal framework. Part III introduces the required PDE methods. The final part of the book, Part IV, is where everything comes together and the power of this approach is presented. It is shown that de Sitter like spacetimes and Minkowski space are stable, static solutions are also discussed. Spatial infinity is discussed and the book finishes by discussing this method in the context of applications to cosmological models and also some numerical methods in GR. This is a highly recommended text for post-graduate students, post-docs and researchers who are interested in conformal method in general relativity. It fills a wide gap in the literature.