Orthogonal Bianchi B stiff fluids close to the initial singularity

TL;DR

This paper extends previous work on orthogonal Bianchi class B perfect fluids near the initial singularity by including stiff fluids, revealing unique convergence behaviors towards the Jacobs set.

Contribution

It fills the gap in understanding the asymptotic behavior of stiff fluids in Bianchi class B models, showing solutions converge to the Jacobs set with distinct dynamics.

Findings

Solutions converge to the Jacobs set in the stiff fluid case.

A full measure set of solutions converges to a specific subset of the Jacobs set.

Convergence behavior differs significantly from the non-stiff case.

Abstract

In our previous article [Rad16], we investigated the asymptotic behaviour of orthogonal Bianchi class B perfect fluids close to the initial singularity and proved the Strong Cosmic Censorship conjecture in this setting. In several of the statements, the case of a stiff fluid had to be excluded. The present paper fills this gap. We work in expansion-normalised variables introduced by Hewitt-Wainwright and find that solutions converge, but show a convergence behaviour very different from the non-stiff case: All solutions tend to limit points in the two-dimensional Jacobs set. A set of full measure, which is also a countable intersection of open and dense sets in the state space, yields convergence to a specific subset of the Jacobs set.