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Oxford Graduate Texts in Mathematics #16: Partial Differential Equations in General Relativity

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Synopses & Reviews

Publisher Comments:

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 in research 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 interest in 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 partial differential 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 of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology.

Book News Annotation:

This textbook on partial differential equations focuses on how this branch of mathematics is being used in general relativity research, especially in regards to matter models and symmetry classes. Rendall (Max Planck Institute for Gravitational Physics, Germany) has developed this material for graduate students and research scientists in mathematics and physics who need to expand their knowledge of Einstein's equations, including asymptomatically flat and spatially compact spacetimes. A chapter in this book also considers the Cauchy problem for Einstein's equations. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

Table of Contents

1. Introduction

2. General relativity

3. Matter models

4. Symmetry classes

5. Ordinary differential equations

6. Functional Analysis

7. Elliptic Equations

8. Hyperbolic Equations

9. The Cauchy problem for the Einstein equations

10. Global results

11. The Einstein-Vlasov Equation

12. The Einstein-scalar field system

Product Details

ISBN:
9780199215416
Author:
Rendall, Alan D.
Publisher:
Oxford University Press, USA
Author:
Rendall, Alan
Subject:
Applied
Subject:
Chemistry - General
Subject:
Mathematics
Subject:
Differential equations, partial
Subject:
Relativity
Subject:
General relativity (Physics) -- Mathematics.
Subject:
Differential Equations - Partial Differential Equations
Subject:
Mathematical Physics
Subject:
Mathematics | Applied Mathematics
Subject:
General-General
Series:
Oxford Graduate Texts in Mathematics
Series Volume:
16
Publication Date:
20080731
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
6 BW Line
Pages:
352
Dimensions:
6.1 x 9.1 x 0.6 in 1 lb

Related Subjects

Health and Self-Help » Health and Medicine » General
Health and Self-Help » Health and Medicine » General Medicine
History and Social Science » World History » General
Science and Mathematics » Physics » Relativity Theory

Oxford Graduate Texts in Mathematics #16: Partial Differential Equations in General Relativity New Trade Paper
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Product details 352 pages Oxford University Press, USA - English 9780199215416 Reviews:
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