Double black hole solutions in Einstein-scalar theory

This paper studies the double black hole solutions in the Einstein-scalar theory and finds that, unlike in vacuum General Relativity, the theory allows for balanced static, neutral, asymptotically flat double black hole solutions where the scalar field provides the equilibrium repulsion. These solutions are scalar hairy versions of the double Schwarzschild (or Bach-Weyl) solution and are regular both above and below the (topological spherical) horizons. We give an explicit construction using a Weyl-type structure that is applicable for numerical solutions and does not require partial linearization or integrability structures of the Einstein-scalar equations. Fixing the model coupling, the balanced configurations form a one-parameter family of solutions, labeled by the proper distance between the black holes.