One Ring to Rule Them All ... and in the Darkness Bind Them?

TL;DR

The work addresses the microstate structure of the three-charge BPS black hole in eleven-dimensional supergravity by constructing all BPS three-charge solutions preserving the same supersymmetries. It introduces a linear system on $R^4$ with self-dual fluxes $G_i$ ($G_i = * G_i$), warp factors $Z_i$, and rotation one-form $k$, enabling explicit generation of black rings and supertubes with arbitrary closed profiles. The main contributions include a complete solution framework, explicit $U(1)\times U(1)$ symmetric rings, and the demonstration that black rings abundantly violate black-hole uniqueness; many of these geometries may map to microstates of the D1-D5-p system, offering a route to entropy counting via horizonless geometries. The results reinforce the Mathur fuzzball picture by showing that black holes can be viewed as ensembles of regular microstate geometries, while highlighting rich phenomenology such as bound-state questions, horizon topology changes, and CFT interpretations.

Abstract

We construct all eleven-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries. Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects. We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial R^4 transverse to the branes. The black rings copiously violate black hole uniqueness. The supertube solutions are completely regular, and generically have small curvature. They also have the same asymptotics as the three-charge black hole; and so they might be mapped to microstates of the D1-D5-p system and used to explain the entropy of this black hole.