Quantum-corrected thermodynamics and P-V criticality of self-gravitating Skyrmion black holes

Abstract

We study the quantum-corrected thermodynamics of a class of black holes generated by self-gravitating Skyrmion models. One such black hole solution is the Einstein-Skrymion black hole. We first compute the Arnowitt-Deser-Misner mass of an Einstein-Skyrmion black hole using an on-shell Hamiltonian formalism already present in the literature. We then consider nonextended phase space thermodynamics and derive expressions for various thermodynamic quantities like the Hawking temperature, entropy, pressure, Gibbs free energy, and heat capacity. Next, we study the effect of quantum corrections on the thermodynamics of the Einstein-Skyrmion black hole. We observe that apart from leading to stability, the quantum correction induces an anti-de Sitter to de Sitter phase transition in the Einstein-Skrymion black hole. Treating the cosmological constant as the pressure, we determine the P-V criticality of the Einstein-Skrymion black hole and observe that it depends on the model parameters λ and K. This study of the P-V criticality could help to estimate the experimental bound on the values of λ and K.