Effective thermodynamics and critical phenomena of rotating regular-de Sitter black holes

Abstract

We consider the horizon structure of a rotating regular-de Sitter (dS) black hole, which has an additional parameter k because of nonlinear electrodynamics (NED) apart from its mass (M) and angular momentum (a). The rotating regular de Sitter black holes, like Kerr dS black holes, admit a cosmological horizon (rc) beside the inner Cauchy (r−) and outer event (rh) horizons. Considering the relation between rh and rc, we analyze the effective thermodynamic quantities associated with rotating regular dS black holes. The expressions for the effective temperature and the effective pressure are obtained, and plotted for various values of k. The second order phase transition for thermodynamic stability is marked by the divergence of the heat capacity of constant pressure CP, the volume expansion coefficient α, and the isothermal compressibility κT at multiple critical points xc = rh/rc with the stable (unstable) branch with positive (negative) heat capacity. It turns out that at a critical point, the heat capacity of constant pressure, the isothermal compressibility, and the volume expansion coefficient of the rotating regular dS black holes exhibit an infinite peak suggesting a second order phase transition. Our results, in the absence of a charge from the NED (k = 0), vis-à-vis go over to that of Kerr dS black holes.