Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006
© 2006 European Mathematical Society
The Cauchy problem in General Relativity
Igor Rodnianski
Abstract
The paper revisits some of the classical and recent results on the Cauchy problem in General Relativity. Special emphasis is put on the problems concerning existence of a Cauchy development, break-down criteria and stability. The author would like to make a disclaimer that despite its general title the paper is not intended as a comprehensible survey. Due to the space-time constraints many remarkable results and developments are either mentioned briefly or not discussed at all. Most notably this concerns various work on the Einstein equations with matter and symmetry reduced problems.
Mathematics Subject Classification (2000). Primary 83C05; Secondary 35L15.
Keywords. Einstein equations, existence, break-down, stability.
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