Analytic description of singularities in Gowdy spacetimes

TL;DR

This paper uses Fuchsian Reduction to analytically construct and analyze singular solutions in Gowdy spacetimes, providing detailed asymptotics and confirming previous formal expansions.

Contribution

It introduces a method to construct and analyze Gowdy spacetime singularities with maximum arbitrary functions, extending understanding of their asymptotic behavior.

Findings

Solutions have Kasner-like singularities with precise asymptotics.

Solutions with velocity parameter > 1 are not observed numerically.

Provides justification for formal expansions by Grubii7 and Moncrief.

Abstract

We use Fuchsian Reduction to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized, or other known solutions. The method provides precise asymptotics at the singularity, which is Kasner-like. All of these solutions are asymptotically velocity-dominated. The results account for the fact that solutions with velocity parameter uniformly greater than one are not observed numerically. They also provide a justification of formal expansions proposed by Grubi\v{s}i\'c and Moncrief.