Stability of AVTD Behavior Within the Polarized $$\mathbb {T}{}^2$$-Symmetric Vacuum Spacetimes

We prove stability of the family Kasner solutions within class polarized $$\mathbb {T}{}^2$$ -symmetric vacuum Einstein equations in contracting time direction with respect to an areal foliation. All for which asymptotic velocity parameter K satisfies $$|K-1|>2$$ are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically term dominated (AVTD) behavior blow-up Kretschmann scalar.