Higher dimensional black holes and supersymmetry

TL;DR

The paper addresses whether supersymmetric black holes in five-dimensional minimal supergravity are uniquely determined by their asymptotic charges, motivated by non-uniqueness in higher dimensions such as black rings. It employs the general SUSY solution structure and a detailed near-horizon analysis to derive two theorems: (1) any SUSY solution with a compact horizon has a near-horizon geometry locally isometric to flat space, $AdS_3 imes S^2$, or the BMPV near-horizon geometry, and (2) under an additional global assumption (the SUSY Killing vector is timelike outside the horizon), the only asymptotically flat SUSY black hole with BMPV-like near-horizon geometry is the BMPV black hole itself. Together, these results support the entropy calculations by reinforcing the uniqueness of SUSY black holes in the studied class, while acknowledging the broader landscape may include exotic solutions like black rings. The work also outlines avenues for extending the approach to other supergravity theories and highlights open questions about possible AdS$_3 imes S^2$ near-horizon geometries.

Abstract

It has recently been shown that the uniqueness theorem for stationary black holes cannot be extended to five dimensions. However, uniqueness is an important assumption of the string theory black hole entropy calculations. This paper partially justifies this assumption by proving two uniqueness theorems for supersymmetric black holes in five dimensions. Some remarks concerning general properties of non-supersymmetric higher dimensional black holes are made. It is conjectured that there exist new families of stationary higher dimensional black hole solutions with fewer symmetries than any known solution.