Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant. (2nd May 2022) - Ames, Ellery; Beyer, Florian; Isenberg, James; Oliynyk, Todd A.
Abstract : We prove the nonlinear stability of the asymptotic behaviour of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarized T 2 -symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constant Λ . This stability result generalizes the results proven in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T 2 -symmetric vacuum spacetimes. Ann. Henri Poincaré . (doi:10.1007/s00023-021-01142-0 )), which focus on the Λ = 0 case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even for Λ = 0, the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarized T 2 -symmetric vacuum solutions than those considered in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T 2 -symmetric vacuum spacetimes. Ann. Henri Poincaré . (doi:10.1007/s00023-021-01142-0 )) and Fournodavlos G et al. (2020 Stable Big Bang formation for Einstein's equations: the complete sub-critical regime . Preprint. (http://arxiv.org/abs/2012.05888 )). Our results establish that the areal time coordinate takes all values in ( 0, T 0 ] for some T 0 > 0, for certain families of polarized T 2 -symmetric solutions with cosmological constant. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.