English

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 T2T^2-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 KK satisfies K1>2|K-1|>2 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