Equilibrium configurations of two charged masses in general relativity

An asymptotically flat static solution of Einstein-Maxwell equations which describes the field of two nonextreme Reissner-Nordström sources in equilibrium is presented. It is expressed in terms of physical parameters of the sources (their masses, charges, and separating distance). Very simple analytical forms were found for the solution as well as for the equilibrium condition which guarantees the absence of any struts on the symmetry axis. This condition shows that the equilibrium is not possible for two black holes or for two naked singularities. However, in the case when one of the sources is a black hole and another one is a naked singularity, the equilibrium is possible at some distance separating the sources. It is interesting that for appropriately chosen parameters even a Schwarzschild black hole together with a naked singularity can be “suspended” freely in the superposition of their fields.