Exact fields of charge and mass distributions in general relativity

Abstract

Presented in this paper are exact solutions to Einstein’s field equations generated via static spherically symmetric mass and charge distributions. In the limit in which the mass density vanishes but the charge density does not, the mass seen by an observer at infinity does not vanish and the metric exterior to the source can be the Ressner-Nordstrom or Schwarzschild solution depending upon the charge distribution. This mass, generated by the energy density of the electromagnetic field, cannot be set equal to zero for a body of finite size. If the charge is concentrated in a thin shell and the charge and mass as seen by an observer at infinity are set equal to those of an electron, the radius of the shell is half the classical electron radius. Finally, we exhibit a class of solutions in which the red-shift (from a point in the body to infinity) is maximum at the surface rather than at the center.