# Microstate geometries at a generic point in moduli space

## TL;DR

This paper classifies supersymmetric solutions in six-dimensional (2,0) supergravity with null isometry, showing that solutions with at least four supersymmetries are not new and have implications for microstate geometries of black holes.

## Contribution

It demonstrates that all solutions with at least four supersymmetries are also solutions of a (1,0) theory, indicating no genuinely new solutions in this class.

## Key findings

- Solutions with ≥4 supersymmetries are also solutions of (1,0) theory.
- Supersymmetric microstate geometries of single-center black holes have only one compact 3-cycle.
- No new solutions with these properties can be found in this framework.

## Abstract

We systematically study all supersymmetric solutions of six-dimensional (2,0) supergravity with a null isometry. In particular, every such solution with at least four real supersymmetries is also a supersymmetric solution of a (1,0) theory preserving the same absolute amount of supersymmetry. This implies that no genuinely new solutions of this type can be found in this framework. The microstate geometries associated to supersymmetric black holes within Mathur's proposal are generically supersymmetric solutions of six-dimensional supergravity. A direct consequence of our result is that supersymmetric microstate geometries of single centre supersymmetric black holes should carry only one compact 3-cycle.