A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model
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.
Keywords
Cite
@article{arxiv.1304.8042,
title = {A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model},
author = {Ikjyot Singh Kohli and Michael C. Haslam},
journal= {arXiv preprint arXiv:1304.8042},
year = {2014}
}