On The Equilibrium Configuration of Two Reissner-nordstrom Objects and Repulsive Gravity

A family of static asymptotically flat exact solutions for the Einstein-Maxwell equations that describe the field of two electrically charged massive objects (the Reissner - Nordstrom sources without any struts or strings between them) in equilibrium is discussed. The equilibrium is possible only when one of the sources is a black hole and the other is a naked singularity or when both sources are extreme black holes (Majumdar-Papapetrou situation). It is interesting that for a sufficiently short distance between the sources, even a neutral Schwarzshild black hole can "hang" freely in the field of a naked singularity; it seems that this phenomenon arises only due to the naked singularity creating a repulsive gravity effect. We stress that the repulsive gravity effect is not specifically due the naked singularity because regular matter sources exhibiting the same phenomena exist. One such source in the form of the Nambu-Coto spherically symmetric membrane is described. The point is that the membrane is able to cut out the central naked singularity region and at the same time to join in an appropriate way the Reissner-Nordstrom repulsive region.