The mass of a static charged sphere

Abstract

The field of a static, charged sphere is investigated using general relativity. InNordström's exterior solution the parametersm ande, referring to mass and charge, are unrelated, and indeedm can be put equal to zero. It is shown that, if the interior solution is considered,m cannot be put zero unless the matter density is negative. The contribution of the electric field energy to the gravitational mass is estimated using certain special models.

A model is given in which the gravitational attraction of the charged matter balances its electrical repulsion. If the radius is allowed to tend to zero, this gives a model of a point charge with finite and non-zero mass and charge.