Partial Differential Equations in General Relativity (Paperback)

Paperback. A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role inresearch on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interestin general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partialdifferential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field ofmathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology. A text that will bring together PDE theory, general relativity and astrophysics to deliver an overview of theory of partial differential equations for general relativity. The text will include numerous examples and provide a unique resource for graduate students in mathematics and physics, numerical relativity and cosmology. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…