# More on microstate geometries of 4d black holes

## TL;DR

This paper constructs explicit microstate geometries for 4D black holes using D-brane configurations, revealing complex moduli spaces and smooth horizon-free solutions in five dimensions.

## Contribution

It provides explicit examples of microstate geometries with detailed constraints, advancing understanding of black hole microstates in string theory.

## Key findings

- Explicit microstate geometries constructed for 4D black holes
- Moduli space includes disjoint components with finite volume
- Solutions are smooth and horizon-free in five dimensions

## Abstract

We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in $\mathbb{R}^3$. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.