Hairy black holes in the general Skyrme model

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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.