Geometric Engineering 5d Black Holes with Rod Diagrams

TL;DR

This paper explores how rod diagrams can be used to analyze the topology and singularities of static 5-dimensional black hole solutions, introducing a novel black lens with unique properties and singularities.

Contribution

It introduces a new static 5D black hole solution with lens space topology, analyzed via rod diagrams, and discusses its singularities and thermodynamic properties.

Findings

The black lens has a lens space horizon topology.

The solution is asymptotically Minkowski without quotients.

It contains naked spherical curvature singularities.

Abstract

Static solutions of 5-dimensional gravity with two spatial Killing vectors are characterized by their rod structures. In this note we describe how the orbifold singularities and the topologies of the horizons and asymptotic regions can be determined from the corresponding rod diagrams. As an example we introduce the black lens, a static 5-dimensional black hole with a horizon of lens space topology which is asymptotically Minkowski space. The solution is novel in that the asymptotic Minkowski space is not quotiented. However it suffers from a naked singularity. While the conical and orbifold singularities have been removed, two spherical curvature singularities remain. These singularities do not contribute to the ADM mass, and the thermodynamics of the black lens is well behaved, although its entropy is lower than that of a Tangherlini black hole of the same mass.