Model for an electrostatic capacitor in Einstein-Maxwell theory
A general relativistic model of a parallel-plate electrostatic capacitor is presented. The spacetime is a solution to the Einstein--Maxwell equations and involves class of solution previously studied by Veselý and Žofka (VŽ). In particular, the parts containing curvature singularities are cut out and the remaining regular section is glued to asymptotically-Minkowski spacetimes. In essence, this results in a curved electro-vacuum VŽ spacetime sandwiched on both sides by exterior spacetimes with vanishing electromagnetic fields. Junction conditions require the presence of charged matter on the boundaries. We interpret this configuration as a parallel-plate capacitor with gravitational effects induced by the strong electric fields. The spherical capacitor is briefly considered.