Two black holes attached to strings

An axisymmetric solution of the Einstein-Maxwell equations is found which represents the static placement of two charged black holes of equal mass (M) and opposite charge (±Q) with ∣Q∣ > M. The space-time, external to the event horizons of the two black holes, is asymptotically flat and entirely smooth except for the occurrence, on the axis, of a simple conical singularity with deficit. In other words, a ‘string’ stretches along the axis of symmetry and provides support for the black holes. In the extended space-time, interior to the horizons of the black holes, time-like curvature singularities, with two spatial dimensions, do occur. And, finally, the surface gravity that prevails on the horizons of the two black holes vanishes. This transgression of the two theorems, excluding the existence of multiple black holes except those of the extreme Reissner–Nordström type and requiring |Q| ≼ M for isolated black holes, is made possible by relaxing the strict requirements of smoothness to the extent of allowing conical singularities. The solution obtained in this paper is, at the classical level, analogous to the equilibrium solution one has found, at the quantal level, for Dirac magnetic monopoles connected by strings.