Two Schwarzschild-like black holes balanced by their scalar hair

We show that, unlike vacuum general relativity, Einstein-scalar theories allow balanced static, neutral, asymptotically flat, double-black hole solutions, for scalar field models minimally coupled to gravity, with appropriate self-interactions. These are scalar hairy versions of the double-Schwarzschild (or Bach-Weyl) solution, but regular on and outside the two (topologically spherical) horizons. The balancing repulsive force is provided by the scalar field. An explicit illustration is presented, using a Weyl-type construction adapted to numerical solutions, requiring no partial linearization, or integrability structure, of the Einstein -scalar equations. Fixing the couplings of the model, the balanced configurations form a one-parameter family of solutions, labeled by the proper distance between the black holes.