# Counting Superstrata

## TL;DR

This paper counts and analyzes superstrata solutions in supergravity that serve as microstates for the D1-D5-P black hole, finding they are insufficient to account for the black hole's entropy and suggesting the need for more complex configurations.

## Contribution

It provides a count of superstrata solutions and assesses their role as black hole microstates, highlighting missing modes and proposing directions for future research.

## Key findings

- Superstrata solutions are fewer than expected for black hole microstates.
- Entropy of superstrata is parametrically smaller than the black hole entropy.
- Higher and fractional modes are missing in current superstrata models.

## Abstract

We count the number of regular supersymmetric solutions in supergravity, called superstrata, that represent non-linear completion of linear fluctuations around empty AdS_3 x S^3. These solutions carry the same charges as the D1-D5-P black hole and represent its microstates. We estimate the entropy using thermodynamic approximation and find that it is parametrically smaller than the area-entropy of the D1-D5-P black hole. Therefore, these superstrata based on AdS_3 x S^3 are not typical microstates of the black hole. What are missing in the superstrata based on AdS_3 x S^3 are higher and fractional modes in the dual CFT language. We speculate on what kind of other configurations to look at as possible realization of those modes in gravity picture, such as superstrata based on other geometries, as well as other brane configurations.