Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

TL;DR

This paper investigates the local dynamics and gravitational collapse of a magnetized self-gravitating Fermi gas using Einstein-Maxwell equations in a Bianchi-I spacetime, revealing conditions for stable attractors and singularities.

Contribution

It introduces a dynamical systems approach to analyze the collapse of a magnetized Fermi gas, highlighting the role of initial conditions and magnetic fields in the evolution and singularity formation.

Findings

Trajectories reach a stable attractor with negative initial expansion.

Positive initial expansion leads to curvature singularities, either isotropic or anisotropic.

Large magnetic fields can produce anisotropic line singularities aligned with the magnetic field.

Abstract

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3-dimensional sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H_{0} is negative. If H_{0} is positive, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular "point") or anisotropic (singular "line"). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the "line" points in the same direction of the field.