In this article, we extend the numerical studies developed in [Periodic analogues of the Kerr solutions: A numerical study, Classical Quantum Gravity 40, 175010 (2023).] to construct periodic stationary axisymmetric solutions containing multiple horizons in each fundamental domain. As a direct application, we consider periodic stationary axisymmetric solutions with two identical equidistant counterrotating horizons. These solutions can be parametrized by the period $L$, the mass $M$, and the absolute value of the angular momentum $|J|>0$. We provide strong numerical evidence for the existence of such configurations, without any restriction in terms of the distance between horizons. This is in sharp contrast with the nonzero total angular momentum case, as it was recently established in [Static vacuum $3+1$ black holes that cannot be put into stationary rotation, Classical Quantum Gravity 42, 085008 (2025).] that static single-horizon periodic solutions cannot be put into rotation if $L<4M$. It is shown that these solutions do not have any struts on the axis, and it is also explicitly shown that, by taking nonequidistant horizons, struts develop between the black holes. Other global properties of the solutions are also presented.

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• Classical black holes
• General relativity equations & solutions