Thermodynamic phase transitions and compressibility of rotating Bardeen(–AdS) black holes with quintessence

Abstract

We derive thermodynamic quantities such as the Hawking temperature, mass, entropy, heat capacity and study the thermodynamic phase transitions of rotating Bardeen black holes surrounded by quintessence-like matter. Interpreting the cosmological parameter as thermodynamic pressure and its conjugate variable as volume, the first law of black hole thermodynamics has been modified in the Anti-de Sitter (AdS) space. It then has been used to investigate the thermodynamics of the rotating Bardeen–AdS black hole with quintessence matter. Properties of the thermodynamic volume have also been analyzed through the study of compressibility and sound speed of the black hole. The black hole sound speed is associated with the adiabatic compressibility, and it equals the light speed for nonrotating black holes and decreases with increasing angular momentum. The nonrotating black holes are adiabatically incompressible, and as the angular momentum attains a maximum value in the extremal case, the compressibility grows maximum. We further derive the equation of state in the extended phase space and explore the critical behaviors of the black hole in the canonical ensemble. Graphs of phase transitions and critical behaviors show an accentuated influence of quintessence matter on the thermodynamic phase transitions and stability of the black holes and support the van der Waals-like phase transition behavior.