Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometry

Abstract

We use qualitative arguments combined with numerical simulations to argue that, in the approach to the singularity in a vacuum solution of Einstein's equations with $T^2$ isometry, the evolution at a generic point in space is an endless succession of Kasner epochs, punctuated by bounces in which either a curvature term or a twist term becomes important in the evolution equations for a brief time. Both curvature bounces and twist bounces may be understood within the context of local mixmaster dynamics although the latter have never been seen before in spatially inhomogeneous cosmological spacetimes.

Corrected typo in Eq. (15)

References in corpus (3)

• Analytic description of singularities in Gowdy spacetimes
• Manufacture of Gowdy spacetimes with spikes
• Asymptotic Behavior in Polarized {\bf T}${}^2$-symmetric Vacuum Spacetimes

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