In charged Einstein-Maxwell initial data sets, a boundary surface must have area at least a sharp function of its electric charge and the cosmological constant, with equality only for product geometries.
Galloway, Rigidity and positivity of mass for asymptotically hyperbolic manifolds , Ann
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Area-charge inequalities and rigidity of time-symmetric initial data sets
In charged Einstein-Maxwell initial data sets, a boundary surface must have area at least a sharp function of its electric charge and the cosmological constant, with equality only for product geometries.