Two asymptotically flat spinning black holes balanced by their self-interacting, synchronized scalar hair
Phys. Rev. D 114, 044063 – Published 20 August, 2026
DOI: https://doi.org/10.1103/d7mg-1zhq
Abstract
Asymptotically flat balanced configurations of two spinning black holes with synchronized scalar hair (2sBHs) are possible [Carlos A. R. Herdeiro and Eugen Radu, Two spinning black holes balanced by their synchronized scalar hair, Phys. Rev. Lett. 131, 121401, 2023]. 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. In all cases, the two components are identical, carrying equal mass and angular momentum. Here, we investigate the effects of quartic scalar self-interactions on this family of solutions, comprising the 2sBSs, the 2sBHs, and an intermediate family: single spinning black holes 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 [Carlos A. R. Herdeiro and Eugen Radu, Dynamical formation of Kerr black holes with synchronized hair: An analytic model, Phys. Rev. Lett. 119, 261101 (2017) , Yves Brihaye, Thomas Delplace, Carlos Herdeiro, and Eugen Radu, An analytic effective model for hairy black holes, Phys. Lett. B 782, 124 (2018)]. 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.
