Black Lenses in Kaluza-Klein Matter

TL;DR

This paper constructs the first explicit examples of asymptotically flat black holes with lens space topologies in higher dimensions, supported by Kaluza-Klein matter, expanding the known landscape of black hole solutions.

Contribution

It introduces a novel method to generate regular higher-dimensional black hole solutions with arbitrary lens space topologies supported by Kaluza-Klein matter.

Findings

First explicit solutions with lens space horizons in 5D

Regular solutions without conical singularities

Method applicable to any dimension for various topologies

Abstract

We present the first examples of formally asymptotically flat black hole solutions with horizons of general lens space topology $L(p,q)$. These 5-dimensional static/stationary spacetimes are regular on and outside the event horizon for any choice of relatively prime integers $1\leq q<p$, in particular conical singularities are absent. They are supported by Kaluza-Klein matter fields arising from higher dimensional vacuum solutions through reduction on tori. The technique is sufficiently robust that it leads to the explicit construction of regular solutions, in any dimension, realising the full range of possible topologies for the horizon as well as the domain of outer communication, that are allowable with multi-axisymmetry. Lastly, as a by product, we obtain new examples of regular gravitational instantons in higher dimensions.