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arXiv · 2203.16656

A local rigidity theorem for minimal two-spheres in an electrovacuum spacetime

Halyson Baltazar·Abdênago Barros·Rondinelle Batista
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Abstract

The purpose of this article is to prove that, under suitable constrains on the electrovacuum spacetime $M$, if $\Sigma\subset M$ is an embedded strictly stable minimal two-sphere which locally maximizes the charged Hawking mass, then there exist a neighborhood of it in $M$ isometric to the Reissner-Nordstr\"om-de Sitter space. At the same time, motived by \cite{Brendle}, we will deduce an estimate for area of a two-sphere which is locally area minimizing in an electrovacuum spacetime. Moreover, if the equality holds, then there exist a neighborhood of it in $M$ isometric to the charged Nariai space.

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Halyson Baltazar, Abdênago Barros, Rondinelle Batista. 2022-03-30. A local rigidity theorem for minimal two-spheres in an electrovacuum spacetime. https://arxiv.org/abs/2203.16656

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