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Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes

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arxiv 2101.03167 v3 pith:TAT2C4QG submitted 2021-01-08 gr-qc

Ellery Ames , Florian Beyer , James Isenberg , Todd Oliynyk This is my paper · ORCID
classification gr-qc
keywords solutionsavtdbehaviorkasnerpolarizedstabilitysymmetrictime
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abstract

We prove stability of the family of Kasner solutions within the class of polarized $T^2$-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 $K$ satisfies $|K-1|>2$ are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.

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Cited by 1 Pith paper

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  1. Stability of Big Bang singularity for the Einstein-Maxwell-scalar field-Vlasov system in the full strong sub-critical regime

    gr-qc 2025-07 conditional novelty 7.0 of 10

    Nonlinear stability of Kasner Big Bang singularities is proved for the Einstein-Maxwell-scalar field-Vlasov system throughout the full strong sub-critical range of Kasner exponents.

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