Dynamics of magnetic Bianchi VI_0 cosmologies

TL;DR

This paper uses dynamical systems methods to demonstrate that magnetic fields in Bianchi VI_0 vacuum cosmologies induce oscillatory behavior near singularities, with solutions exhibiting at least two Kasner points and a curvature singularity.

Contribution

It provides a rigorous analysis showing magnetic fields fundamentally alter the approach to singularities in Bianchi VI_0 models, introducing oscillatory dynamics.

Findings

Magnetic fields cause oscillatory evolution toward singularity.

Solutions' alpha-limit sets include multiple Kasner points.

All magnetic solutions have curvature singularities.

Abstract

Methods of dynamical systems analysis are used to show rigorously that the presence of a magnetic field orthogonal to the two commuting Killing vector fields in any spatially homogeneous Bianchi type VI_0 vacuum solution to Einstein's equation changes the evolution toward the singularity from convergent to oscillatory. In particular, it is shown that the alpha-limit set (for time direction that puts the singularity in the past) of any of these magnetic solutions contains at least two sequential Kasner points of the BKL sequence and the orbit of the transition solution between them. One of the Kasner points in the alpha-limit set is non-flat, which leads to the result that each of these magnetic solutions has a curvature singularity.