Stable isoperimetric surfaces in super-extreme Reissner-Nordstr\"om

TL;DR

This paper investigates the properties and stability of isoperimetric surfaces in Reissner-Nordström spacetime, establishing bounds on their area in relation to charge, and deriving inequalities for stable surfaces in electro-vacuum initial data.

Contribution

It provides new bounds on the area-charge relationship for isoperimetric surfaces and analyzes their stability in super-extreme Reissner-Nordström spacetime.

Findings

Lower bound on area in terms of charge

Inequality saturation at extremal transition

General area-charge inequality for stable surfaces

Abstract

We study isoperimetric surfaces in the Reissner-Nordstr\"om spacetime, with emphasis on the cuasilocal inequality between area and charge. We analyze the stability of the isoperimetric spheres and we found that there is a lower bound on the area in terms of the charge, and that the inequality is saturated in the transition from the superextremal to the subextremal case. We also derive a general inequality between area and charge for stable isoperimetric surfaces in maximal electro-vacuum initial data.