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

Abstract

It is well known that there are the black hole horizon and the cosmological horizon for the ReissnerNordström-de Sitter (RN-dS) spacetime. The thermodynamic quantities on the both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are some additional connections between them. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in (n + 2)-dimensional RN-dS 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 the 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 a liquid-gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid-gas systems.

A note on entropy of de Sitter black holes

“…A discussion of the relation between the Friedman equation and the Cardy formula can be found in [33]. We also refer the reader to [34] for a discussion of the phase transition of de Sitter black holes using the aforementioned effective thermal equilibrium state.…”

Circular orbit of a test particle and phase transition of a black hole

“…Specifically, we here will focus on a special kind of the circular orbit, named as the ISCO [42][43][44][45][46][47][48][49][50][51][52]. To obtain parameters (such as radius r i ) of the ISCO, we should add one another condition V e (r i ) = 0 (32) to the effective potential Eq. (12) of the particle-black hole system, which claims that the maximal and the minimal values of the effective potential merge at the ISCO radius r i .…”

“…After using the constraint conditions Eqs. (13), (14) and (32) for the effective potential Eq. (38), one can obtain the radius r i of ISCO which can be expressed as a function of mass M , electric charge Q, and AdS radius l, as…”

Black holes and Boyle's law — The thermodynamics of the cosmological constant

“…The positive Λ case has in D > 4 has so far received very little attention, though charged black holes were shown to have phase transitions in [135].…”