Hairy black holes in the general Skyrme model

Abstract

We study the existence of hairy black holes in the generalized Einstein-Skyrme model. It is proven that in the Bogomol'nyi-Prasad-Sommerfield 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 L4. As an example, we show that there are no hairy black holes in the L2+L6+L0 model and present a new kind of black hole solutions with compact Skyrmion hair in the L4+L6+L0 model.