Extended thermodynamics of self-gravitating skyrmions

A modification of the hedgehog ansatz has recently lead to novel exact black hole solutions with selfgravitating SU(2) Skyrme fields. Considering a negative cosmological constant the black holes are not asymptotically anti-de Sitter (AdS) but rather asymptote to an AdS version of Barriola-Vilenkin spacetime. We examine the thermodynamics of the system interpreting the cosmological constant as a bulk pressure. We use the standard countertenn method to obtain a finite Euclidean action. For a given coupling of the matter action the system behaves as does a charged AdS black hole in the fixed charged ensemble. We find that in the limit case when the Skyrme model becomes a nonlinear sigma model the system exhibits a first order phase transition of Hawking-Page type. The universality class of these Einstein-Skyrme black holes is that of van der Waals.