Periodic Analogs of Multiple Black Holes Solutions

TL;DR

This paper constructs and numerically studies periodic solutions with multiple black hole horizons, demonstrating their existence without horizon distance restrictions and analyzing their physical properties.

Contribution

It extends previous numerical methods to find periodic multi-horizon black hole solutions with rotation, showing their existence and properties without horizon distance constraints.

Findings

Existence of periodic multi-horizon solutions with rotation confirmed.

Solutions have no struts on the axis, unlike non-equidistant horizon configurations.

Global properties of these solutions are characterized.

Abstract

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.