Zero area singularities in general relativity and inverse mean curvature flow

TL;DR

This paper explores Zero Area Singularities in general relativity, examining their mass properties using inverse mean curvature flow to establish new relationships with ADM mass and capacity.

Contribution

It introduces new results linking Zero Area Singularities' mass to the ADM mass and capacity through inverse mean curvature flow techniques.

Findings

Established bounds on the mass of Zero Area Singularities

Connected the singularity mass with ADM mass of the manifold

Analyzed the capacity of Zero Area Singularities

Abstract

First we restate the definition of a Zero Area Singularity, recently introduced by H. Bray. We then consider several definitions of mass for these singularities. We use the Inverse Mean Curvature Flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity.