Area-charge inequalities and rigidity of time-symmetric initial data sets

TL;DR

This paper derives new area-charge inequalities for time-symmetric Einstein-Maxwell initial data sets, leading to rigidity theorems that extend classical results to charged scenarios using innovative geometric techniques.

Contribution

It introduces novel area-charge inequalities and rigidity theorems for charged initial data sets, employing Gromov's μ-bubble method in a new geometric context.

Findings

Established new area-charge inequalities for boundary of initial data sets.

Proved rigidity theorems with no uncharged analogues.

Applied Gromov's μ-bubble technique in a novel setting.

Abstract

In this paper, we establish new area-charge inequalities for the boundary of time-symmetric Einstein-Maxwell initial data sets, in both compact and noncompact cases, under the dominant energy condition. These inequalities lead to novel rigidity theorems with no analogues in the uncharged setting. In the noncompact case, our result is obtained by applying Gromov's $\mu$-bubble technique in a new geometric context.