Asymptotic Behavior of the $T^3 \times R$ Gowdy Spacetimes

TL;DR

This paper provides perturbative evidence supporting the strong cosmic censorship conjecture in Gowdy T^3 spacetimes, showing that most initial data lead to curvature singularities near the boundary of maximal Cauchy development.

Contribution

It introduces the 'geodesic loop solution' as the dominant term in Einstein's equations near singularities, extending understanding of spacetime behavior in Gowdy models.

Findings

Most initial data lead to curvature singularities.

The dominant term is a solution with all spatial derivatives dropped.

Perturbative results are partially rigorously justified.

Abstract

We present new evidence in support of the Penrose's strong cosmic censorship conjecture in the class of Gowdy spacetimes with $T^3$ spatial topology. Solving Einstein's equations perturbatively to all orders we show that asymptotically close to the boundary of the maximal Cauchy development the dominant term in the expansion gives rise to curvature singularity for almost all initial data. The dominant term, which we call the ``geodesic loop solution'', is a solution of the Einstein's equations with all space derivatives dropped. We also describe the extent to which our perturbative results can be rigorously justified.