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arXiv · 2108.02886

Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant

Ellery Ames·Florian Beyer·James Isenberg·Todd Oliynyk
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Abstract

We prove the nonlinear stability of the asymptotic behavior of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarised $T^2$-symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constant $\Lambda$. This stability result generalizes the results proven in [3], which focus on the $\Lambda=0$ case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even for $\Lambda=0$, the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarised $T^2$-symmetric vacuum solutions than those considered in [3] and [26]. Our results establish that the areal time coordinate takes all values in $(0, T_0]$ for some $T_0 > 0$, for certain families of polarised $T^2$-symmetric solutions with cosmological constant.

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Ellery Ames, Florian Beyer, James Isenberg, Todd Oliynyk. 2021-08-05. Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant. https://doi.org/10.1098/rsta.2021.0173

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