A Reformulation of the Hoop Conjecture

TL;DR

This paper proposes a new geometric reformulation of the Hoop Conjecture using trapped circles, addressing compactness and superposition issues, and introduces a novel inequality and conjecture related to black hole horizons.

Contribution

It introduces a reformulated Hoop Conjecture based on trapped circles, resolving key issues and proposing new geometric inequalities and horizon properties.

Findings

A new geometric Hoop inequality is proposed.

Problems of compactness and superposition are addressed.

A conjecture on peeling properties of horizons is introduced.

Abstract

A reformulation of the Hoop Conjecture based on the concept of trapped circle is presented. The problems of severe compactness in every spatial direction, and of how to superpose the hoops with the surface of the black hole, are resolved. A new conjecture concerning "peeling" properties of dynamical/trapping horizons is propounded. A novel geometric Hoop inequality is put forward. The possibility of carrying over the results to arbitrary dimension is discussed.