Phase Structures and Transitions of Quintessence Surrounding RN Black Holes in a Grand Canonical Ensemble

TL;DR

This paper investigates the phase structures and transitions of Reissner-Nordström black holes surrounded by quintessence dark energy in both AdS space and a Dirichlet wall, revealing distinct phase behaviors and transitions.

Contribution

It provides a comparative analysis of black hole phase transitions in two different boundary conditions with detailed parameter space exploration.

Findings

First-order phase transition occurs at lower potential in AdS space.

Multiple phase transition types are identified in the Dirichlet wall scenario.

Distinct phase regions are mapped out for different boundary conditions.

Abstract

Considering a grand canonical ensemble, we study the phase structures and transitions of RN black holes surrounded by quintessence dark energy on two different boundary conditions, namely AdS space and a Dirichlet wall. For AdS space, under the condition of fixed temperature and potential, as the temperature increases for lower potential, the black hole undergoes a first-order phase transition, while for higher potential, no phase transition occurs. There are two different regions in the parameter space. For the Dirichlet wall, on which the temperature and potential are fixed and the state parameter of quintessence $\omega=-2/3$ is analyzed in detail. Then, three different physically allowed regions in the parameter space of the black hole are well studied. As the temperature rises, a first-order phase transition and a second-order phase transition may occur. In this case, there are nine regions in the parameter space, which is obviously distinct from the case of AdS space.