Thermodynamics of rotating Bardeen black holes: Phase transitions and thermodynamics volume

We investigate the thermodynamical properties of the rotating Bardeen black holes characterized by mass m , the spin parameter a , and the magnetic charge g . We calculate exact expressions of the Hawking temperature, mass, entropy, and heat capacity. The black hole mass is minimum at radius r_+E, where both the heat capacity and temperature vanish with a stable remnant. Also, there exists a critical radius r_+C of multiple orders, where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range r_+E<r₊<r_+C. We also analyze the extended phase space thermodynamics of the rotating Bardeen-anti-de Sitter black holes. Treating the cosmological constant Λ and charge g as thermodynamic variables, we derive the generalized first law in the extended phase space to study the critical phenomena of the black holes. The Ehrenfest scheme for the P -V criticality of the rotating Bardeen black holes in anti-de Sitter spaces is examined. The Clausius-Clapeyron-Ehrenfest equations confirming the second-order phase transitions of the van der Waals fluid is no longer valid.