Two Schwarzschild-like black holes balanced by their scalar hair

TL;DR

This paper demonstrates that Einstein-scalar theories can produce balanced double-black hole solutions with scalar hair, where the scalar field provides the repulsive force to maintain equilibrium, extending classical solutions in General Relativity.

Contribution

It introduces new balanced double-black hole solutions with scalar hair in Einstein-scalar theories, constructed without linearization or integrability assumptions.

Findings

Balanced solutions form a one-parameter family based on black hole separation.

Scalar hair provides the necessary repulsive force for equilibrium.

Solutions are regular outside and on the horizons, extending classical double-black hole configurations.

Abstract

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 linearisation, or integrability structure, of the Einstein-scalar equations. Fixing the couplings of the model, the balanced configurationsform a one-parameter family of solutions, labelled by the proper distance between the black holes.