Dynamics of a self--gravitating magnetized source

TL;DR

This paper studies the evolution of a magnetized degenerate fermion gas in an anisotropic universe, revealing that it always evolves from a singularity to a stable attractor, with initial anisotropies depending on initial conditions.

Contribution

It provides a qualitative and numerical analysis of Einstein-Maxwell equations for a magnetized fermion gas in Bianchi I spacetime, identifying the asymptotic behavior and attractors.

Findings

Initial anisotropic singularities evolve into stable attractors.

The singularity type depends on initial conditions, being 'cigar' or 'plate'.

The system's evolution is governed by a non-linear autonomous set of equations.

Abstract

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I spacetime with a Kasner--like metric. We examine the dynamics of this system by means of a qualitative and numerical study of Einstein-Maxwell field equations which reduce to a non--linear autonomous system. For all initial conditions and combinations of free parameters the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the ``cigar'' or ``plate'' types.