# On Bianchi type VI$_0$ spacetimes with orthogonal perfect fluid matter

## TL;DR

This paper analyzes the early-time behavior of Bianchi type VI$_0$ spacetimes with perfect fluid matter, confirming a conjecture about their initial singularity being vacuum dominated, anisotropic, and silent, and explores related Klein-Gordon equation asymptotics.

## Contribution

It proves Wainwright's conjecture on the nature of initial singularities in Bianchi VI$_0$ spacetimes and extends understanding of their asymptotic properties.

## Key findings

- Initial singularity is vacuum dominated, anisotropic, and silent for generic solutions.
- Convergence results for Klein-Gordon solutions on these backgrounds are established.
- The conjecture about the initial singularity is confirmed.

## Abstract

We study the asymptotic behaviour of Bianchi type VI$_0$ spacetimes with orthogonal perfect fluid matter satisfying Einstein's equations. In particular, we prove a conjecture due to Wainwright about the initial singularity of such spacetimes. Using the expansion-normalized variables of Wainwright-Hsu, we demonstrate that for a generic solution the initial singularity is vacuum dominated, anisotropic and silent. In addition, by employing known results on Bianchi backgrounds, we obtain convergence results on the asymptotics of solutions to the Klein-Gordon equation on all backgrounds of this type, except for one specific case.