Dynamics of Bianchi type I elastic spacetimes

TL;DR

This paper analyzes the global dynamics of Bianchi type I elastic spacetimes, showing solutions isotropize over time but oscillate near the singularity, with implications for anisotropic matter models in cosmology.

Contribution

It introduces a dynamical systems approach to Bianchi I elastic spacetimes and demonstrates isotropization and oscillatory behavior near singularities.

Findings

Solutions isotropize toward the future.

Solutions oscillate near the initial singularity.

Solutions do not settle into Kasner states but oscillate between them.

Abstract

We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotropic matter model that naturally generalizes perfect fluids. Based on our dynamical systems formulation of the equations we are able to prove that (i) toward the future all solutions isotropize; (ii) toward the initial singularity all solutions display oscillatory behavior; solutions do not converge to Kasner solutions but oscillate between different Kasner states. This behavior is associated with energy condition violation as the singularity is approached.