Thermodynamics of the Reissner-Nordstr\"om-de Sitter Spacetime with Quintessence

TL;DR

This paper investigates the thermodynamics and phase transitions of Reissner-Nordström-de Sitter black holes with quintessence, revealing Van der Waals-like behavior and the role of entropic force in spacetime evolution.

Contribution

It introduces the interaction between black hole and cosmological horizons in RNdS spacetime with quintessence, analyzing phase transitions and entropic forces from a micro perspective.

Findings

Spacetime exhibits Van der Waals-like phase transition behavior.

Isochoric heat capacity remains non-zero, completing the thermodynamic description.

Entropic force influences the evolution and interaction of horizons.

Abstract

For Anti-de Sitte (AdS) black holes, the isochoric heat capacity of system is vanished, while the isobaric heat capacity is not. However, this situation does not hold on for de Sitter (dS) black holes. In this work, by introducing the interaction between the black hole horizon and the cosmological horizon of the Reissner-Nordstr\"om-de Sitter (RNdS) spacetime with quintessence, we discuss the phase transition of this system. The results show that the spacetime not only has the similar phase transition behavior to that of Van der Waals (VdW) system, and the non-vanishing isochoric heat capacity fulfills the whole thermodynamics system. Through the discussion of the entropic force between two horizons, we find out the role of entropic force in the evolution of spacetime. In addition, we also study the influence of various parameters on the phase transition and entropic force, which will provide a new method for exploring the interaction among black hole molecules from a micro perspective.