Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$

TL;DR

This paper extends previous work on the Einstein-Vlasov system by removing symmetry assumptions, demonstrating that non-diagonal Bianchi types II and VI$_0$ solutions are asymptotically diagonal in the future.

Contribution

It removes the reflection symmetry assumption, handling the non-diagonal case of Bianchi types II and VI$_0$ in Einstein-Vlasov systems.

Findings

Non-diagonal solutions become asymptotically diagonal over time.

Methods are robust enough to handle increased complexity without symmetry.

Results generalize previous diagonal case stability analysis.

Abstract

In a recent paper arXiv:1208.4231 we have treated the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change the future of the non-diagonal spacetimes in consideration is asymptotically diagonal.