Brown-York mass and the hoop conjecture in non-spherical massive systems

TL;DR

This paper explores the connection between Brown-York mass concentration and trapped surface formation in non-spherical systems, formulating and proving a version of the hoop conjecture in conformally flat geometries.

Contribution

It introduces a precise formulation and proof of the hoop conjecture for non-spherical systems using Brown-York mass and conformally flat geometries.

Findings

Established a relationship between total rest mass and Brown-York mass.

Proved a version of the hoop conjecture in non-spherical, conformally flat geometries.

Extended previous spherical symmetry results to more general geometries.

Abstract

We discuss the relation between the concentration of the Brown-York mass and the formation of trapped surfaces in non-spherical massive systems. In particular, we formulate and prove a precise version of the Thorne hoop conjecture in conformally flat three-geometries sliced by equipotential foliation leaves. An intriguing relationship between the total rest mass and the Brown-York mass is shown. This is a further investigation of the previous work on the Brown-York mass hoop conjecture in spherical symmetry.