Thermodynamics and phase transition of rotating regular-de Sitter black holes

Abstract

We analyze thermodynamic properties of the rotating regular black holes having mass (M), angular momentum (a), and a magnetic charge (g), and encompass Kerr black hole ($g=0$). The mass M has a minimum at the radius $r_+=r_+^{\star }$, where both the heat capacity and temperature vanish. The thermal phase transition is because of the divergence of heat capacity at a critical radius $r_{+}^{C}$ with stable (unstable) branches for $r_+<r_+^{C}$ ($>r_+^{C}$). We also generalize the rotating regular black holes in de Sitter (dS) background and analyzed its horizon structure to show that for each g, there are two critical values of the mass parameter $M_{\text {cr1}}$ and $M_{\text {cr2}}$ which correspond to the degenerate horizons. Thus, we have rotating regular-dS black holes with an additional cosmological horizon apart from the inner (Cauchy) and the outer (event) horizons. Next, we discuss the effective thermodynamic quantities of the rotating regular-dS black holes in the extended phase space where the cosmological constant ($\Lambda$) is considered as thermodynamic pressure. Combining the first laws at the two horizons, we calculate the heat capacity at constant pressure $C_\mathrm{P}$, the volume expansion coefficient $\alpha$, and the isothermal compressibility $\kappa _\mathrm{T}$. At a critical point, the specific heat at constant pressure, the volume expansion coefficient, and the isothermal compressibility of the regular-dS black holes exhibit an infinite peak suggesting a second-order phase transition.