Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity

TL;DR

This paper extends Fuchsian analysis to Gowdy spacetimes without requiring analyticity, enabling detailed descriptions of singularities in smooth cases, thus broadening the applicability of the technique.

Contribution

It develops a method to remove the analyticity assumption in Fuchsian equations, applying it to Gowdy spacetimes to establish results in the smooth category.

Findings

Analytic results are extended to smooth Gowdy spacetimes.

The method demonstrates potential for broader applications beyond analyticity.

Strengths and weaknesses of the approach are discussed.

Abstract

Fuchsian equations provide a way of constructing large classes of spacetimes whose singularities can be described in detail. In some of the applications of this technique only the analytic case could be handled up to now. This paper develops a method of removing the undesirable hypothesis of analyticity. This is applied to the specific case of the Gowdy spacetimes in order to show that analogues of the results known in the analytic case hold in the smooth case. As far as possible the likely strengths and weaknesses of the method as applied to more general problems are displayed.