Dynamics of a self-gravitating neutron source

TL;DR

This paper models the dynamics of a magnetized neutron gas under self-gravity within a Bianchi I spacetime, revealing singularity formation through numerical solutions of Einstein-Maxwell equations.

Contribution

It formulates the Einstein-Maxwell equations as a 4D dynamical system for a neutron gas in a Bianchi I universe and analyzes its evolution.

Findings

Numerical solutions show the emergence of a point-like singularity.

The model provides insights into neutron gas collapse in compact objects.

The approach offers a fully relativistic analysis of neutron gas dynamics.

Abstract

We examine the dynamics of a self--gravitating magnetized neutron gas as a source of a Bianchi I spacetime described by the Kasner metric. The set of Einstein-Maxwell field equations can be expressed as a dynamical system in a 4-dimensional phase space. Numerical solutions of this system reveal the emergence of a point--like singularity as the final evolution state for a large class of physically motivated initial conditions. Besides the theoretical interest of studying this source in a fully general relativistic context, the resulting idealized model could be helpful in understanding the collapse of local volume elements of a neutron gas in the critical conditions that would prevail in the center of a compact object.