Double-Reissner-Nordström solution and the interaction force between two spherical charged masses in general relativity

Abstract

The physical representation of the general double--Reissner--Nordstr\"om solution is obtained by rewriting the $N=2$ Bret\'on--Manko--Aguilar electrostatic metric in the Varzugin--Chistyakov parametrization $({M}_{i},{Q}_{i},R)$. A concise analytical formula is derived for the interaction force between two arbitrary Reissner--Nordstr\"om constituents, and an example of the equilibrium configuration involving two oppositely charged particles which confirms earlier Bonnor's prediction of the existence of such configurations is given.