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

TL;DR

This paper constructs five-dimensional vacuum solutions with axial symmetry using inverse scattering, revealing that certain solutions correspond to known black ring configurations with rotation.

Contribution

It demonstrates how to generate five-dimensional black ring solutions via inverse scattering from Minkowski seed spacetime, connecting solitonic methods with known black hole geometries.

Findings

Generated solutions match known black ring solutions with one angular momentum.

The inverse scattering method effectively produces physically relevant five-dimensional vacuum solutions.

The approach links solitonic techniques to higher-dimensional black hole physics.

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.