Thermodynamics of phase transition in higher dimensional Reissner-Nordström-de Sitter black hole

Abstract

It is well known that there are black hole and the cosmological horizons for the Reissner-Nordström-de Sitter spacetime. Although the thermodynamic quantities on the horizons are not irrelevant, they satisfy the laws of black hole thermodynamics respectively. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in $(n+2)$-dimensional Reissner-Nordström-de Sitter spacetime. The thermodynamic properties of these effective quantities are analyzed, moreover, the critical temperature, critical pressure and critical volume are obtained. We carry out an analytical check of Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the spacetime undergoes a second order phase transition at the critical point. This result is consistent with the nature of liquid--gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid--gas systems.

18 pages, 7 figures, 1 table

References in corpus (4)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• Thermodynamics of de Sitter Black Holes: Thermal Cosmological Constant
• Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole

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