# Extended Thermodynamics of Self-Gravitating Skyrmions

## TL;DR

This paper explores the thermodynamics of novel self-gravitating Skyrme black holes with a negative cosmological constant, revealing phase transitions similar to van der Waals fluids and extending understanding of black hole thermodynamics.

## Contribution

It introduces a modified ansatz leading to new black hole solutions with unique thermodynamic properties, including phase transitions and universality classes.

## Key findings

- Black holes behave like charged AdS black holes in thermodynamics.
- Discovery of a Hawking--Page type phase transition.
- Black holes exhibit van der Waals universality class.

## Abstract

A modification of the hedgehog ansatz has recently led 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 counterterm 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.