Two asymptotically flat spinning black holes balanced by their self-interacting, synchronised scalar hair

TL;DR

This paper explores how quartic scalar self-interactions influence balanced configurations of two spinning black holes with scalar hair, revealing effects on ergoregion topology, solution 'hairiness', and bifurcation structures.

Contribution

It introduces the impact of scalar self-interactions on the properties and structure of two spinning black holes with scalar hair, extending previous models.

Findings

Self-interactions cause a topological transition of the ergoregion in boson stars.

Increased self-interaction strength makes solutions 'hairier' without increasing horizon mass.

Self-interactions reshape bifurcation structures and influence horizon mass fractions.

Abstract

Asymptotically flat balanced configurations of two spinning black holes with synchronised scalar hair (2sBHs) are possible (arXiv:2305.15467). These are constructed within a generalized Bach-Weyl framework and arise from two spinning boson stars (2sBSs) by placing a horizon at the center of each component. Here, we investigate the effects of quartic scalar self-interactions on this family of solutions, comprising the 2sBSs, the 2sBHs, and an intermediate configuration--single spinning black hole with quadrupolar scalar hair (1sBHs). For 2sBSs, the additional repulsive force introduced by the self-interactions drives a topological transition of the ergoregion, from a single torus to a double torus, in the strong-gravity regime. For 1sBHs, as the self-interaction coupling strength increases, the solutions become "hairier" but their horizons cannot become heavier; moreover, the self-interactions broaden the regime in which an analytical effective model accurately describes these solutions. For 2sBHs, increasing the coupling reshapes the bifurcation structure of the solution sequences and, as in the 1sBH case, repulsive self-interactions cannot make the horizons heavier; horizons carrying a larger mass fraction are obtained only when attractive self-interactions are considered.