# A stationary and biaxisymmetric four-soliton solution in five dimensions

## TL;DR

This paper constructs a new exact five-dimensional black hole solution with biaxial symmetry using inverse scattering, revealing configurations with lens space horizons and analyzing special cases with zero or one angular momentum.

## Contribution

It introduces a novel four-soliton solution in five-dimensional vacuum Einstein equations, including a rotating black hole with lens space topology, expanding the set of known exact solutions.

## Key findings

- Solution includes a rotating black hole with lens space horizon topology.
- Parameter analysis reveals degrees of freedom related to mass and angular momenta.
- Special cases include static and single-angular-momentum black holes.

## Abstract

Using the inverse scattering method to solve the five-dimensional vacuum Einstein equations, we construct an asymptotically flat four-soliton solution as a stationary and bi-axisymmetric solution. We impose certain boundary conditions on this solution so that it includes a rotating black hole whose horizon-cross section is topologically a lens space of L(2,1). The solution has nine parameters but three only is physically independent due to the constraint equations. The remaining degrees of freedom correspond to the mass and two independent angular momenta of the black hole. We analyze a few simple cases in detail, in particular, the static case with two zero-angular momenta and the stationary case with a single non-zero angular momentum.