Hairy black holes in the general Skyrme model

TL;DR

This paper investigates the existence of hairy black holes within the generalized Einstein-Skyrme model, demonstrating the necessity of the Skyrme term for such solutions and introducing new black hole solutions with compact Skyrmion hair.

Contribution

It proves the absence of hairy black holes in the BPS limit and shows that the Skyrme term is essential for their existence, also presenting new solutions with compact Skyrmion hair.

Findings

No hairy black holes in the BPS limit.

Skyrme term $ ext{L}_4$ is necessary for hairy black holes.

New black hole solutions with compact Skyrmion hair.

Abstract

We study the existence of hairy black holes in the generalized Einstein-Skyrme model. It is proven that in the BPS model limit there are no hairy black hole solutions, although the model admits gravitating (and flat space) solitons. Furthermore, we find strong evidence that a necessary condition for the existence of black holes with Skyrmionic hair is the inclusion of the Skyrme term $\mathcal{L}_4$. As an example, we show that there are no hairy black holes in the $\mathcal{L}_2+\mathcal{L}_6+\mathcal{L}_0$ model and present a new kind of black hole solutions with compact Skyrmion hair in the $\mathcal{L}_4+\mathcal{L}_6+\mathcal{L}_0$ model.