Second-order hyperbolic Fuchsian systems. Gowdy spacetimes and the Fuchsian numerical algorithm - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: This is the second part of a series devoted to the singular initial valueproblem for second-order hyperbolic Fuchsian systems. In the first part, wedefined and investigated this general class of systems, and we established awell-posedness theory in weighted Sobolev spaces. This theory is applied hereto the vacuum Einstein equations for Gowdy spacetimes admitting, by definition,two Killing fields satisfying certain geometric conditions. We recover, by moredirect and simpler arguments, the well-posedness results established earlier byRendall and collaborators. In addition, in this paper we introduce a naturalapproximation scheme, which we refer to as the Fuchsian numerical algorithm andis directly motivated by our general theory. This algorithm provides highlyaccurate, numerical approximations of the solution to the singular initialvalue problem. In particular, for the class of Gowdy spacetimes underconsideration, various numerical experiments are presented which show theinterest and efficiency of the proposed method. Finally, as an application, wenumerically construct Gowdy spacetimes containing a smooth, incomplete,non-compact Cauchy horizon.



Author: Florian Beyer, Philippe G. LeFloch

Source: https://arxiv.org/







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