# No skyrmion hair for stationary spherically symmetric reflecting stars

## TL;DR

This paper demonstrates that unlike black holes, stationary spherically symmetric reflecting stars cannot support skyrmion hair, highlighting a fundamental difference in their field configurations.

## Contribution

The study proves the absence of skyrmion hair in reflecting stars within the Einstein Skyrme system, contrasting with known black hole solutions.

## Key findings

- No skyrmion hair for reflecting stars
- Contrast with black hole skyrmion solutions
- Supports uniqueness of reflecting star configurations

## Abstract

We investigate the existence of the skyrmion field in the background of an asymptotically flat stationary reflecting star. For this purpose, we consider the Einstein Skyrme system for which there is a skyrmion hair in the black hole case. We discuss spherically symmetric skyrmions and employ the hedgehog ansatz for the skyrmion field. We show that, in contrast to the black hole there is no skyrmion hair for a reflecting star.