Charged spheres in general relativity

Abstract

The Einstein–Maxwell equations for a spherically symmetric distribution of charged matter are studied. A general equation is derived for the rate of change of the "total energy" of the sphere in terms of the 4–4 component of the electromagnetic and matter tensors. It is shown that, subject to certain conditions, the spheres of charged matter can oscillate, and further that the static configuration is uniquely given by the relation m2 = 4πe2α, where [Formula: see text]. Finally, it is demonstrated that the equilibrium configuration is unstable to small radial perturbations.