Holomorphic Waves of Black Hole Microstructure

TL;DR

This paper constructs extensive families of smooth, horizonless supergravity solutions with the same charges as black holes, using holomorphic functions to simplify their structure and demonstrate their regularity, with implications for dual CFTs.

Contribution

It introduces a holomorphic framework for constructing and analyzing superstratum solutions, expanding the known families and simplifying their mathematical description.

Findings

Constructed the largest families of smooth superstrata to date.

Reformulated BPS equations in holomorphic form for simplicity.

Discovered solutions with localized momentum waves and spread into the IR.

Abstract

We obtain the largest families constructed to date of $\tfrac{1}{8}$-BPS solutions of type IIB supergravity. They have the same charges and mass as supersymmetric D1-D5-P black holes, but they cap off smoothly with no horizon. Their construction relies on the structure of superstratum states, but allows the momentum wave to have an arbitrary shape. Each family is based on an arbitrary holomorphic function of one variable. More broadly, we show that the most general solution is described by two arbitrary holomorphic functions of three variables. After exhibiting several new families of such "holomorphic superstrata," we reformulate the BPS backgrounds and equations in holomorphic form and show how this simplifies their structure. The holomorphic formulation is thus both a fundamental part of superstrata as well as an effective tool for their construction. In addition, we demonstrate that holomorphy provides a powerful tool in establishing the smoothness of our solutions without constraining the underlying functions. We also exhibit new families of solutions in which the momentum waves of the superstrata are highly localized at infinity but diffuse and spread into the infra-red limit in the core of the superstratum. Our work also leads to some results that can be tested within the dual CFT.