Periodic Kerr solution as an infinite soliton chain
Phys. Rev. D 112, 044006 – Published 5 August, 2025
DOI: https://doi.org/10.1103/mhb9-mhjt
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 behavior 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 Peraza et al. [Classical Quantum Gravity 40, 175010 (2023).] based on the heat flow, together with analytic results by Peraza and Reiris [Classical Quantum Gravity 42, 085008 (2025).] 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 one to completely describe the existence domain in the space of physical parameters (the period, mass, and angular momentum); we study the dependence of Kasner exponent and the shape of the ergosphere on parameters of the problem.
