  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.
