A unified hoop conjecture for black holes and horizonless compact stars

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 $4πM_{in}/C\leqslant 1$, 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.

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