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This is a Quantitative Study study.

October 19, 2025Open Access

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

TCTiarlos CruzUniversidade Federal de Alagoas AMAbraão MendesUniversidade Federal de Alagoas

Key Points

New area-charge inequalities provide insights into time-symmetric Einstein-Maxwell initial data sets, indicating unique rigidity theorems.
The results demonstrate novel properties that differ significantly from uncharged settings, offering fresh perspectives in the field.
Application of Gromov's μ-bubble technique reveals new geometric contexts in proving inequalities for both compact and noncompact scenarios.
Findings underline the importance of the dominant energy condition in establishing structural properties of the data sets analyzed.

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 μ-bubble technique in a new geometric context.

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