# Supersymmetric black hole non-uniqueness in five dimensions

## TL;DR

This paper systematically explores five-dimensional supersymmetric black hole solutions, revealing multiple solutions with identical charges but different topologies and entropies, including the first nonspherical black hole with BMPV-like charges.

## Contribution

It provides a complete analysis of three-centered solutions with a single black hole, discovering new topologies and entropy properties, and demonstrating non-uniqueness in five-dimensional supersymmetric black holes.

## Key findings

- Identified four solutions with the same charges as BMPV black hole.
- Discovered a black lens with L(3,1) topology as a non-spherical solution.
- Found solutions with higher entropy than BMPV near the spin bound.

## Abstract

We present a systematic study of the moduli space of asymptotically flat, supersymmetric and biaxisymmetric black hole solutions to five-dimensional minimal supergravity. Previously, it has been shown that such solutions must be multi-centred solutions with a Gibbons-Hawking base. In this paper we perform a full analysis of three-centred solutions with a single black hole, for which there are seven regular black hole solutions. We find that four of these can have the same conserved charges as the BMPV black hole. These consist of a black lens with L(3,1) horizon topology and three distinct families of spherical black holes with nontrivial topology outside the horizon. The former provides the first example of a nonspherical black hole with the same conserved charges as the BMPV black hole. Moreover, of these four solutions, three can have a greater entropy than the BMPV black hole near the BMPV upper spin bound. One of these is a previously known spherical black hole with nontrivial topology and the other two are new examples of a spherical black hole with nontrivial topology and an L(3,1) black lens.