English

Orthogonal Bianchi B stiff fluids close to the initial singularity

General Relativity and Quantum Cosmology 2017-12-13 v2 Mathematical Physics Differential Geometry math.MP

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.

Keywords

Cite

@article{arxiv.1712.02699,
  title  = {Orthogonal Bianchi B stiff fluids close to the initial singularity},
  author = {Katharina Radermacher},
  journal= {arXiv preprint arXiv:1712.02699},
  year   = {2017}
}

Comments

29 pages, v2: minor typos, layout changes

R2 v1 2026-06-22T23:11:17.603Z