One Thousand and One Bubbles

TL;DR

This paper introduces a systematic method for constructing five-dimensional microstate geometries on Gibbons-Hawking spaces, enabling the discovery of new solutions with complex configurations and minimal angular momentum, advancing understanding of black hole microstates.

Contribution

The authors develop a novel, systematic approach to generate all five-dimensional BPS microstate geometries on Gibbons-Hawking bases, including solutions with non-Abelian fields and minimal angular momentum.

Findings

Expanded spectrum of scaling solutions with non-Abelian fields

Explicit construction of a 50-center solution

First smooth microstate geometries with arbitrarily small angular momentum

Abstract

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.