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

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.

arXiv comment28 pages. Fixed minor typos and made several clarifications. Agrees with published version

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Cited by in corpus (6)

• Stable Big Bang formation for Einstein's equations: The complete sub-critical regime
• Localized big bang stability for the Einstein-scalar field equations
• Stress and Geometry for Isotropic Singularities
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant
• Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity
• Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability