Bianchi Class B Spacetimes with Electromagnetic Fields

TL;DR

This paper analyzes Bianchi Class B cosmological spacetimes with electromagnetic fields, identifying stable vacuum plane-wave solutions and exploring their relation to perturbations of open FLRW universes.

Contribution

It provides a detailed dynamical system analysis of Bianchi Class B spacetimes with electromagnetic fields, including new exact solutions and their implications.

Findings

Vacuum plane-wave solutions are stable attractors for expanding universes.

Some solutions are newly identified and not previously published.

Vacuum plane-wave modes relate to long-wavelength electromagnetic perturbations.

Abstract

We carry out a thorough analysis on a class of cosmological spacetimes which admit three space-like Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those solutions, we discuss the relation between those homogeneous models and perturbations of open FLRW universes. We argue that the vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations.