Magnetic tension and gravitational collapse

TL;DR

This paper explores how magnetic tension influences gravitational collapse, revealing that magnetic field properties can oppose collapse and potentially prevent singularity formation without violating energy conditions.

Contribution

It provides a qualitative analysis of magnetic tension effects on collapse, highlighting the role of magneto-curvature stress in resisting gravitational contraction.

Findings

Magnetic field winding aids collapse through tension.

Shear distortions in magnetic gradients resist contraction.

Magneto-curvature stress can prevent focusing of worldlines.

Abstract

The gravitational collapse of a magnetised medium is investigated by studying qualitatively the convergence of a timelike family of non-geodesic worldlines in the presence of a magnetic field. Focusing on the field's tension we illustrate how the winding of the magnetic forcelines due to the fluid's rotation assists the collapse, while shear-like distortions in the distribution of the field's gradients resist contraction. We also show that the relativistic coupling between magnetism and geometry, together with the tension properties of the field, lead to a magneto-curvature stress that opposes the collapse. This tension stress grows stronger with increasing curvature distortion, which means that it could potentially dominate over the gravitational pull of the matter. If this happens, a converging family of non-geodesic lines can be prevented from focusing without violating the standard energy conditions.