Periodic Kerr solution as an infinite soliton chain

TL;DR

This paper uses inverse scattering and numerical analysis to explore the periodic Kerr solution, modeling it as an infinite soliton chain, and maps out the parameter space for its existence and properties.

Contribution

It introduces an efficient inverse scattering method approach to analyze the periodic Kerr solution as an infinite soliton chain, detailing the existence domain and physical characteristics.

Findings

Existence domain of periodic Kerr solutions mapped in parameter space

Dependence of Kasner exponent on solution parameters

Shape and properties of the ergosphere analyzed

Abstract

We combine numerical analysis with the inverse scattering method to study the periodic analog of Kerr solution. The periodic analog of the Schwarzschild solution is known to be regular and exhibit Kasner asymptotic behaviour for an arbitrary size of event horizon not exceeding the period. The previous numerical analysis of the rotating version of the periodic Schwarzschild black hole in [arXiv:2210.12898] based on the heat flow, together with analytical results in [arXiv:2407.16960] shows that there exist obstructions to putting the periodic Schwarzschild solution in rotation in a certain parameter range. In this paper we apply an efficient numerical approach based on the inverse scattering method, interpreting the periodic Kerr solution as an infinite chain of solitons. This allows to completely describe the existence domain in the space of physical parameters (the period, mass and the angular momentum); we study the dependence of Kasner exponent and the shape of the ergosphere on parameters of the problem.