Two Spinning Black Holes Balanced by Their Synchronized Scalar Hair

Abstract

General relativity minimally coupled to a massive, free, complex scalar field, is shown to allow asymptotically flat solutions, nonsingular on and outside the event horizon, describing two spinning black holes (2sBHs) in equilibrium, with coaxial, aligned angular momenta. The 2sBHs configurations bifurcate from solutions describing dipolar spinning boson stars. The BHs emerge at equilibrium points diagnosed by a test particle analysis and illustrated by a Newtonian analog. The individual BH "charges" are mass and angular momentum only. Equilibrium is due to the scalar environment, acting as a (compact) dipolar field, providing a lift against their mutual attraction, making the 2sBHs (h)airborne. We explore the 2sBHs domain of solutions and its main features.