Periodic Kerr solution as an infinite soliton chain

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.