A unified hoop conjecture for black holes and horizonless compact stars

TL;DR

This paper introduces a unified hoop conjecture applicable to both black holes and horizonless compact stars, relating mass and circumference to predict horizon formation.

Contribution

It proposes a new, unified criterion for horizon formation that applies to various compact objects, extending the traditional hoop conjecture.

Findings

The conjecture is expressed as $4\pi M_{in}/C \,\leqslant\, 1$.

It applies to both black holes and horizonless stars.

Provides a quantitative condition for horizon formation.

Abstract

We propose a unified version of hoop conjecture valid for various black holes and horizonless compact stars. This conjecture is expressed by the mass to circumference ratio $4\pi M_{in}/C\leqslant 1$, where C is the circumference of the smallest ring that can engulf the object in all azimuthal directions and $M_{in}$ is the mass within the engulfing sphere.