How hairy can a black ring be?

TL;DR

Horowitz and Reall critically assess the Bena–Warner claim that supersymmetric five-dimensional black-ring solutions can be specified by arbitrary functions along a curve. Through straight-string and arbitrary-curve analyses within the BW construction, they show that smooth horizons arise only for the constant-density circle, and generic configurations lack a C^2 horizon, implying the absence of infinite hair in this class. Using Fermi normal coordinates and near-horizon expansions, they show how ℓ-dependent acceleration and density data obstruct horizon smoothness unless severely constrained. The work strengthens the no-hair perspective for these solutions, while acknowledging potential insights from horizon-continuity considerations and their relation to microstate counting for related configurations.

Abstract

It has been shown recently that there is a large class of supersymmetric solutions of five-dimensional supergravity which generalize the supersymmetric black ring solution of Elvang et al. This class involves arbitrary functions. We show that most of these solutions do not have smooth event horizons, so they do not provide examples of black objects with infinite amounts of "hair".