On the dynamics of Gowdy space times

TL;DR

This paper investigates the near-singularity behavior of Gowdy spacetimes, demonstrating the prevalence of AVTD solutions and analyzing their asymptotic properties, including special cases where the velocity equals zero or one.

Contribution

It proves the generic existence of AVTD behavior near singularities in Gowdy spacetimes and analyzes detailed asymptotics at critical velocity points.

Findings

AVTD solutions are dense near the singularity.

The set of AVTD solutions with a uniformity condition is open.

Power law solutions exhibit distinct asymptotics at velocity zero or one.

Abstract

We study the behavior near the singularity t=0 of Gowdy metrics. We prove existence of an open dense set of boundary points near which the solution is smoothly "asymptotically velocity term dominated" (AVTD). We show that the set of AVTD solutions satisfying a uniformity condition is open in the set of all solutions. We analyse in detail the asymptotic behavior of "power law" solutions at the (hitherto unchartered) points at which the asymptotic velocity equals zero or one. Several other related results are established.