# Four-center bubbled BPS solutions with a Gibbons-Hawking base

## TL;DR

This paper constructs a large family of smooth, horizonless BPS solutions with four Gibbons-Hawking centers, revealing they nearly saturate the cosmic censorship bound on angular momentum, thus advancing understanding of black hole microstates.

## Contribution

It introduces a systematic method to build four-center bubbled BPS solutions from three-supertube configurations using spectral flows and gauge transformations.

## Key findings

- All four-center solutions have angular momentum around 99% of the cosmic censorship bound.
- The solutions form large families with the same charges and angular momentum as supersymmetric black holes.
- Both analytical and numerical analyses explain the high angular momentum feature.

## Abstract

We construct four-center bubbled BPS solutions with a Gibbons-Hawking base space. We give a systematic procedure to build scaling solutions: starting from three-supertube configurations and using generalized spectral flows and gauge transformations to extend to solutions with four Gibbons-Hawking centers. This allows us to construct very large families of smooth horizonless solutions that have the same charges and angular momentum as supersymmetric black holes with a macroscopically large horizon area. Our construction reveals that all scaling solutions with four Gibbons Hawking centers have an angular momentum at around 99% of the cosmic censorship bound. We give both an analytical and a numerical explanation for this unexpected feature.