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arXiv · 1610.06025

The maximal existence region of the analytic solutions for a class of characteristic Einstein vacuum equations

G. Caciotta·F. Nicolò
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Abstract

The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem, due to the intrinsic hyperbolicity of the Einstein equations. The magnitude of this region depends only on suitable $H_s$ Sobolev norms of the initial data for a fixed $s\leq 7$ and if the initial data are sufficiently small the analytic solution is global. In a previous paper, hereafter "I", we have described a geometric way of writing the vacuum Einstein equations for the characteristic problems we are considering and a local solution in a suitable "double null cone gauge" characterized by the use of a double null cone foliation of the spacetime.

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G. Caciotta, F. Nicolò. 2016-10-19. The maximal existence region of the analytic solutions for a class of characteristic Einstein vacuum equations. https://arxiv.org/abs/1610.06025

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