Cosmologies with a magnetic field, dust, and Lambda

TL;DR

This paper explores exact solutions to Einstein-Maxwell equations with a cosmological constant, focusing on Bianchi type III models with magnetic fields and dust, revealing their singularity and expansion behaviors.

Contribution

It provides new exact solutions for Bianchi type III cosmologies with magnetic fields and dust, analyzing their singularity and expansion dynamics.

Findings

Solutions either start with a singularity and expand or collapse into a singularity.

Parameters in the solutions influence the evolution and physical interpretation.

Magnetic fields and dust have distinct roles near singularities.

Abstract

We investigate exact solutions of the Einstein-Maxwell equations with the cosmological constant where the source of the gravitational field consists of a magnetic field and dust. In particular, we restrict our study to the case of Bianchi type III models. All these solutions either start with a singularity and then expand, or they are initially collapsing and end at a singularity. We discuss the physical meaning of the parameters appearing in the metrics and examine the possible subcases and the relative importance of the dust and the magnetic field as we approach the singularity.