# Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes

## TL;DR

This paper proves the existence and uniqueness of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity, characterizing their topologies and physical charges.

## Contribution

It establishes the existence and uniqueness of near-horizon geometries with specified topologies and charges in 5D minimal supergravity, extending previous classifications.

## Key findings

- All possible bi-axisymmetric near-horizon geometries are shown to exist.
- Uniqueness is proven up to isometry of a specific symmetric space.
- Solutions include various horizon topologies with prescribed physical parameters.

## Abstract

We prove existence of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity. These solutions possess the cross-sectional horizon topology $S^3$, $S^1\times S^2$, or $L(p,q)$ and come with prescribed electric charge, two angular momenta, and a dipole charge (in the ring case). Moreover, we establish uniqueness of these solutions up to an isometry of the symmetric space $G_{2(2)}/SO(4)$.