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Mathematical Problems of General Relativity I
Demetrios Christodoulou, ETH-Zurich, Switzerland
A publication of the European Mathematical Society.
cover
Zurich Lectures in Advanced Mathematics
2008; 157 pp; softcover
Volume: 6
ISBN-10: 3-03719-005-1
ISBN-13: 978-3-03719-005-0
List Price: US$32
Member Price: US$25.60
Order Code: EMSZLEC/6
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General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems.

One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media.

The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in general relativity.

Table of Contents

  • Introduction
  • The laws of general relativity
  • Asymptotic flatness at spacelike infinity and conserved quantities
  • The global stability of Minkowski spacetime
  • Bibliography
  • Index
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