Backreaction in the future behavior of an expanding spacetime

TL;DR

This paper investigates the long-term evolution of certain expanding vacuum spacetimes with $T^2$ symmetry, revealing convergence to a non-vacuum homogeneous spacetime on the universal cover.

Contribution

It introduces a rescaling analysis to study the future behavior of $T^2$-symmetric vacuum spacetimes and demonstrates convergence to a non-vacuum homogeneous spacetime.

Findings

On the universal cover, spacetime converges in $C^0$ topology.

The limit spacetime does not satisfy vacuum Einstein equations.

Provides insights into the asymptotic structure of symmetric vacuum spacetimes.

Abstract

We perform a rescaling analysis to analyze the future behavior of a class of $T^2$-symmetric vacuum spacetimes. We show that on the universal cover, there is $C^0$-convergence to a spatially homogeneous spacetime that does not satisfy the vacuum Einstein equations.