Asymptotic Behavior in Polarized {\bf T}$^2$-symmetric Vacuum Spacetimes

TL;DR

This paper investigates the asymptotic behavior near singularities in a class of polarized T^2-symmetric vacuum spacetimes with non-vanishing twist, revealing they are all asymptotically velocity-term dominated.

Contribution

It applies Fuchsian reduction to analyze non-Gowdy T^2-symmetric solutions with twist, showing their universal asymptotic velocity-term dominated behavior.

Findings

Solutions are asymptotically velocity-term dominated near singularity.

All solutions with maximum arbitrary functions share this asymptotic behavior.

The analysis extends understanding of singularity behavior in polarized T^2-symmetric spacetimes.

Abstract

We use Fuchsian Reduction to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy spacetimes, but their twist does not vanish. The spacetimes are also polarized in the sense that one of the `gravitational degrees of freedom' is turned off. Examining an analytic family of solutions with the maximum number of arbitrary functions, we find that they are all asymptotically velocity-term dominated as one approaches the singularity.