Supersymmetric black holes with a single axial symmetry in five dimensions

TL;DR

This paper classifies five-dimensional supersymmetric black hole and soliton solutions with a single axial symmetry, including new smooth solutions with various horizon topologies, expanding understanding of such spacetimes.

Contribution

It provides the first examples of five-dimensional black holes with exactly one axial Killing field that are smooth outside the horizon and classifies solutions with specific symmetry properties.

Findings

Found new smooth black hole solutions with one axial symmetry

Classified solutions with horizon topologies: S^3, S^1×S^2, and lens spaces

Identified a large moduli space with non-contractible 2-cycles

Abstract

We present a classification of asymptotically flat, supersymmetric black hole and soliton solutions of five-dimensional minimal supergravity that admit a single axial symmetry which `commutes' with the supersymmetry. This includes the first examples of five-dimensional black hole solutions with exactly one axial Killing field that are smooth on and outside the horizon. The solutions have similar properties to the previously studied class with biaxial symmetry, in particular, they have a Gibbons-Hawking base and the harmonic functions must be of multi-centred type with the centres corresponding to the connected components of the horizon or fixed points of the axial symmetry. We find a large moduli space of black hole and soliton spacetimes with non-contractible 2-cycles and the horizon topologies are $S^3$, $S^1\times S^2$ and lens spaces $L(p,1)$.