Rotating and swirling binary black hole system balanced by its gravitational spin-spin interaction
Phys. Rev. D 112, 064034 – Published 15 September, 2025
DOI: https://doi.org/10.1103/3954-766n
Abstract
We present the first exact and analytical solution in general relativity describing an equilibrium configuration for two stationary black holes. The metric models two collinear extremal Kerr black holes immersed in an external and back-reacting rotating tidal drag. The gravitational attraction is balanced by the repulsive gravitational spin-spin interaction generated by the interplay between the black holes’ angular momenta and the rotational background. The new solution is built by embedding the double Kerr metric into a swirling universe by means of the Ehlers transformation. The geometry is completely regular outside the event horizons. Thermodynamic properties of the binary black hole system are studied; the Smarr law, the first law, and the Christodoulou-Ruffini formulas are verified. The microscopic degrees of freedom of the entropy are computed from the dual conformal field theories living on the boundary of the near horizon geometries.
