Periodic Analogs of Multiple Black Holes Solutions

In this article, we extend the numerical studies developed in [arXiv:2210.12898] 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 counter-rotating 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 non-zero total angular momentum case, as it was recently established in \cite{Peraza:2024uto} 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 non-equidistant horizons, struts develop between the black holes. Other global properties of the solutions are also presented.