A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model

TL;DR

This paper analyzes the dynamics of a Bianchi Type I cosmological model with magnetic fields and viscosity, revealing conditions for isotropization and discovering new solutions involving magnetic and viscous effects.

Contribution

It introduces a detailed dynamical systems analysis of viscous magnetohydrodynamic Bianchi Type I models, including new solutions with magnetic fields and viscosity effects.

Findings

Fixed points correspond to Kasner, FLRW, and new viscous magnetic solutions.

Model can isotropize at late times under certain viscosity and equation of state parameters.

New Einstein Field equations solutions involving magnetic fields and viscosity are identified.

Abstract

We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe FLRW solution, and interestingly, a new solution to the Einstein Field equations involving non-zero magnetic fields, and non-zero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.