Reduction without reduction: Adding KK-monopoles to five dimensional stationary axisymmetric solutions

TL;DR

The paper introduces a method to add KK-monopole charge to five-dimensional stationary solutions using SL(3,R) symmetry, enabling the construction of new solutions like a static black ring with monopole charge.

Contribution

It develops a general technique leveraging SL(3,R) invariance to modify asymptotic boundary conditions and add KK-monopole charge to existing solutions.

Findings

Constructed a static black ring with KK-monopole charge.

Developed tools to apply SL(3,R) transformations to inverse scattering solutions.

Provided a systematic method for adding monopole charge to five-dimensional solutions.

Abstract

We present a general method to add KK-monopole charge to any asymptotically flat stationary axisymmetric solution of five dimensional General Relativity. The technique exploits the underlying SL(3,R) invariance of the system by identifying a particular element of the symmetry group which changes the asymptotic boundary condition and adds KK-monopole charge. Furthermore, we develop a set of technical tools which allow us to apply the SL(3,R) transformations to solutions produced by the Inverse Scattering method. As an example of our methods, we construct the exact solution describing a static black ring carrying KK-monopole charge.