Bubbling Supertubes and Foaming Black Holes

TL;DR

This paper constructs smooth, horizonless geometries called bubbling supertubes that resolve black ring singularities, providing new microstate solutions for black holes in string theory.

Contribution

It introduces a method to generate large families of smooth three-charge microstate geometries via geometric transitions, advancing the understanding of black hole microstates.

Findings

Constructed explicit smooth geometries resolving black ring singularities.

Found a large family of microstates parameterized by 6N functions.

Conjectured these geometries account for significant black hole entropy.

Abstract

We construct smooth BPS three-charge geometries that resolve the zero-entropy singularity of the U(1) x U(1) invariant black ring. This singularity is resolved by a geometric transition that results in geometries without any branes sources or singularities but with non-trivial topology. These geometries are both ground states of the black ring, and non-trivial microstates of the D1-D5-P system. We also find the form of the geometries that result from the geometric transition of N zero-entropy black rings, and argue that, in general, such geometries give a very large number of smooth bound-state three-charge solutions, parameterized by 6N functions. The generic microstate solution is specified by a four-dimensional hyper-Kahler geometry of a certain signature, and contains a ``foam'' of non-trivial two-spheres. We conjecture that these geometries will account for a significant part of the entropy of the D1-D5-P black hole, and that Mathur's conjecture might reduce to counting certain hyper-Kahler manifolds.