Magnetized Tolman-Bondi Collapse

TL;DR

This paper studies how weak magnetic fields influence gravitational collapse in inhomogeneous Tolman-Bondi spacetimes, revealing that magnetic stresses can dominate and cause anisotropic contraction during collapse.

Contribution

It introduces an analysis of magnetic effects on gravitational collapse within Tolman-Bondi models, highlighting the dominance of magnetic stresses in late-stage anisotropic contraction.

Findings

Lorentz force dominates late-stage collapse

Magnetic stresses grow faster and resist collapse

Collapse becomes strongly anisotropic due to magnetic effects

Abstract

We investigate the gravitational implosion of magnetized matter by studying the inhomogeneous collapse of a weakly magnetized Tolman-Bondi spacetime. The role of the field is analyzed by looking at the convergence of neighboring particle worldlines. In particular, we identify the magnetically related stresses in the Raychaudhuri equation and use the Tolman-Bondi metric to evaluate their impact on the collapsing dust. We find that, despite the low energy level of the field, the Lorentz force dominates the advanced stages of the collapse, leading to a strongly anisotropic contraction. In addition, of all the magnetic stresses, those that resist the collapse are found to grow faster.