The causal structure of microlocalized Einstein metrics

Details The causal structure of microlocalized Einstein metrics The causal structure of microlocalized Einstein metrics

2001-09-23

arxiv.org/abs/math/0109174v1

Mathematics

Analysis of PDEs

Scientific paper

This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikinal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in our first paper.

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