Mean-stable surfaces in Static Einstein-Maxwell theory

TL;DR

This paper investigates the properties of mean-stable surfaces within static Einstein-Maxwell spacetimes, establishing key geometric constraints and bounds on mass, with implications for the structure and stability of such solutions.

Contribution

It introduces new results linking mean-stability, the zero set of the lapse function, and mass bounds in static Einstein-Maxwell theory, extending understanding of geometric stability in these spacetimes.

Findings

Zero set of lapse function is contained in the horizon boundary.

Nonexistence of stable minimal surfaces inside electrostatic spaces under certain conditions.

ADM mass is bounded above by the Hawking quasi-local mass.

Abstract

In this paper we use the theory of mean-stable surfaces (stable minimal surfaces included) to explore the static Einstein-Maxwell space-time. We first prove that the zero set of the lapse function must be contained in the horizon boundary. Then, we explore some implications of it providing some results of nonexistence of stable minimal surfaces in the interior of an electrostatic space, subject to a certain initial boundary data. We finish by proving that the ADM mass is bounded from above by the Hawking quasi-local mass.