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

TL;DR

This paper investigates the behavior of vacuum spacetimes with $T^2$ isometry near singularities, showing that the evolution is characterized by an oscillatory pattern of Kasner epochs and bounces involving curvature and twist effects.

Contribution

It introduces the concept of twist bounces in inhomogeneous cosmological spacetimes and demonstrates their role alongside curvature bounces in local mixmaster dynamics.

Findings

Endless succession of Kasner epochs near singularity

Identification of twist bounces as a new dynamical feature

Confirmation of local mixmaster behavior in inhomogeneous models

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.