Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
General Relativity and Quantum Cosmology
2022-05-20 v3
Abstract
We prove stability of the family of Kasner solutions within the class of polarized -symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions for which the asymptotic velocity parameter satisfies are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.
Keywords
Cite
@article{arxiv.2101.03167,
title = {Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes},
author = {Ellery Ames and Florian Beyer and James Isenberg and Todd Oliynyk},
journal= {arXiv preprint arXiv:2101.03167},
year = {2022}
}
Comments
28 pages. Fixed minor typos and made several clarifications. Agrees with published version