Scanning the parameter space of collapsing rotating thin shells

TL;DR

This study comprehensively analyzes rotating thin shell collapses in higher dimensions, demonstrating that under the weak energy condition, such shells do not produce naked singularities and respect cosmic censorship.

Contribution

It provides an exact formalism for the dynamics of rotating shells in higher odd dimensions and classifies their trajectories, extending understanding of collapse scenarios and cosmic censorship.

Findings

Rotating shells obeying the weak energy condition do not produce naked singularities.

Bouncing shells with positive pressure can remain outside black holes, respecting cosmic censorship.

Shell trajectories are classified across a wide parameter space, including various equations of state.

Abstract

We present results of a comprehensive study of collapsing and bouncing thin shells with rotation, framing it in the context of the weak cosmic censorship conjecture. The analysis is based on a formalism developed specifically for higher odd dimensions that is able to describe the dynamics of collapsing rotating shells exactly. We analise and classify a plethora of shell trajectories in asymptotically flat spacetimes. The parameters varied include the shell's mass and angular momentum, its radial velocity at infinity, the (linear) equation-of-state parameter and the spacetime dimensionality. We find that plunges of rotating shells into black holes never produce naked singularities, as long as the matter shell obeys the weak energy condition, and so respect cosmic censorship. This applies to collapses of dust shells starting from rest or with a finite velocity at infinity. Not even shells with a negative isotropic pressure component (i.e., tension) lead to the formation of naked singularities, as long as the weak energy condition is satisfied. Endowing the shells with a positive isotropic pressure component allows the existence of bouncing trajectories satisfying the dominant energy condition and fully contained outside rotating black holes. Otherwise any turning point occurs always inside the horizon. These results are based on strong numerical evidence from scans of numerous sections in the large parameter space available to these collapsing shells. The generalisation of the radial equation of motion to a polytropic equation-of-state for the matter shell is also included in an appendix.