The gravitational and electrostatic fields far from an isolated Einstein-Maxwell source

The exterior solution for an arbitrary charged, massive source is studied as a static deviation from the Reissner-Nordström metric This is reduced to two coupled ordinary differential equations for the gravitational and electrostatic potential functions. The homogeneous equations are explicitly solved in the particular caseq²=m², obtaining a multipole expansion with radial hypergeometric dependence for both potentials. In the limiting case of a neutral source, the equations are shown to coincide with recent results by Bondi and Rindler.