Schwarzschild black hole hovering in the field of a Reissner-Nordstrom naked singularity

摘要

We piesent a thiee-parametric family of exact static axisymmetric solutions of Einstein-Maxwell equations which describe a Schwarzschild black hole hovering in the field of an over critically charged Reissner-Noidstrom source (naked singularity). This family of solutions depends on three real (positive) parameters which are the mass m of a Schwarzshild black hole, the mass m* of a naked singularity and the parameter ￡ which characterize the distance separating these sources. The only condition I > m is necessary for separation of the sources The charge of the naked singularity e* providing the equilibrium at this distance and various geometric characteristics of interacting sources in our solutions are functions of these three independent parameters This configuration is stable with respect to displacements of the sources one towards or apart from another along the axis of symmetry.