Vacuum solutions of five dimensional Einstein equations generated by inverse scattering method

TL;DR

This work extends solution-generating techniques to five-dimensional vacuum gravity by applying the Belinski-Zakharov inverse scattering method with a Minkowski seed. Focusing on the one-angular-momentum sector, the authors derive a two-soliton solution that reproduces the Mishima-Iguchi rotating black ring and clarify parameter redundancies arising from isometries. They also analyze regularity constraints and argue that obtaining broader families such as the Emparan-Reall ring may require singular seeds, highlighting both the power and limits of the method in higher dimensions. Overall, the paper demonstrates how integrable techniques can yield exact higher-dimensional black hole spacetimes and maps them onto known solutions, enriching the landscape of five-dimensional gravity solutions.

Abstract

We study stationary and axially symmetric two solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method developed by Belinski and Zakharov. In this generation of the solutions, we use five dimensional Minkowski spacetime as a seed. It is shown that if we restrict ourselves to the case of one angular momentum component, the generated solution coincides with a black ring solution with a rotating two sphere which was found by Mishima and Iguchi recently.