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 ( r c ) beside the inner Cauchy ( r − ) and outer event ( r h ) horizons. Considering the relation between r h and r c , 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 C P , the volume expansion coefficient α , and the isothermal compressibility κ T at multiple critical points x c = r h / r c 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.

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