# Isotropization of Slowly Expanding Spacetimes

## TL;DR

This paper demonstrates that certain homogeneous, massless Einstein-Vlasov spacetimes with Bianchi I symmetry tend to become isotropic over time, approaching a radiative Einstein-deSitter universe, with quantitative rates provided.

## Contribution

It introduces an energy method to quantitatively analyze the isotropization process in massless Einstein-Vlasov models with Bianchi I symmetry.

## Key findings

- Spacetimes isotropize towards the Einstein-deSitter model.
- Quantitative estimates on the rate of isotropization are obtained.
- The models asymptote to a radiative universe.

## Abstract

We show that the homogeneous, massless Einstein-Vlasov system with toroidal spatial topology and diagonal Bianchi type I symmetry for initial data close to isotropic data isotropizes towards the future and in particular asymptotes to a radiative Einstein-deSitter model. We use an energy method to obtain quantitative estimates on the rate of isotropization in this class of models.