An Infinite-Dimensional Family of Black-Hole Microstate Geometries

TL;DR

This paper constructs an explicit, infinite-dimensional family of smooth, horizonless black-hole microstate geometries, demonstrating enhanced entropy storage and revealing non-renormalization properties of the governing equations.

Contribution

It introduces a new class of microstate geometries with infinite-dimensional moduli space, surpassing previous entropy bounds, and shows the equivalence of supergravity and brane probe analyses.

Findings

Constructed the first explicit infinite-dimensional microstate geometry.

Demonstrated entropy enhancement over flat space configurations.

Established non-renormalization of bubble equations across moduli space.

Abstract

We construct the first explicit, smooth, horizonless black-hole microstate geometry whose moduli space is described by an arbitrary function of one variable and is thus infinite-dimensional. This is achieved by constructing the scalar Green function on a simple D6 anti-D6 background, and using this Green function to obtain the fully back-reacted solution for a supertube with varying charge density in this background. We show that this supertube can store parametrically more entropy than in flat space, confirming the entropy enhancement mechanism that was predicted using brane probes. We also show that all the local properties of the fully back-reacted solution can, in fact, be obtained using the DBI action of an appropriate brane probe. In particular, the supergravity and the DBI analysis yield identical functional bubble equations that govern the relative locations of the centers. This indicates that there is a non-renormalization theorem that protects these functional equations as one moves in moduli space. Our construction creates configurations that are beyond the scope of recent arguments that appear to put strong limits on the entropy that can be found in smooth supergravity solutions.