Investigations on hoop conjecture for horizonless spherical charged stars

TL;DR

This paper investigates the validity of the hoop conjecture for horizonless spherical charged stars, finding it can be violated or hold depending on how mass is defined, with implications for understanding compact objects.

Contribution

The study extends the analysis of the hoop conjecture to more general horizonless charged stars using exterior solutions, revealing conditions for its validity.

Findings

Hoop conjecture can be violated for very compact stars when using total ADM mass.

The conjecture holds when using the mass contained within the sphere.

Exterior solutions like Reissner-Nordsr$ ext{"o}$m are sufficient for analysis.

Abstract

For horizonless spherical stars with uniform charge density, the hoop conjecture was tested based on the interior solution. In this work, we are interested in more general horizonless spherical charged stars. We test hoop conjecture using the exterior solution since all types of interior solutions correspond to the same exterior Reissner-Nordsr$\ddot{o}$m solution. Our analysis shows that the hoop conjecture is violated for very compact stars if we express the conjecture with the total ADM mass. And the hoop conjecture holds if we express the conjecture using the mass in the sphere.