A rotating black lens solution in five dimensions

TL;DR

This paper constructs a new five-dimensional black lens solution with L(n,1) topology using inverse scattering, revealing that such solutions inherently contain singularities or conical defects.

Contribution

It introduces the first explicit black lens solution with a simple rod structure and single angular momentum in five dimensions.

Findings

The solution has a conical or curvature singularity.

It is asymptotically flat with a single angular momentum.

The black lens topology is possible within vacuum solutions.

Abstract

It has recently been shown that a stationary, asymptotically flat vacuum black hole in five space-time dimensions with two commuting axial symmetries must have an event horizon with either a spherical, ring or lens-space topology. In this paper, we study the third possibility, a so-called black lens with L(n,1) horizon topology. Using the inverse scattering method, we construct a black lens solution with the simplest possible rod structure, and possessing a single asymptotic angular momentum. Its properties are then analysed; in particular, it is shown that there must either be a conical singularity or a naked curvature singularity present in the space-time.