Constant mean curvature surfaces and area-charge inequality for a spheroidal electrically counterpoised dust spacetime

Abstract

We consider the spacetime presented by Bonnor in 1998, whose matter content is a spheroid of electrically counterpoised dust, in the context of the geometrical inequalities between area and charge. We determine numerically the constant mean curvature surfaces that are candidates to be stable isoperimetric surfaces and analyze the relation between area and charge for them, showing that both a previously proved inequality and a conjectured inequality are far from being saturated. We also show that the maximal initial data has a cylindrical limit where the minimum of the area-charge relation is attained.