Thermodynamic stability of black holes surrounded by quintessence

TL;DR

This paper investigates the thermodynamic stability and phase transitions of black holes surrounded by quintessence, revealing instability in uncharged cases and second-order phase transitions in charged cases, with different thermodynamic descriptions.

Contribution

It introduces effective thermodynamic quantities for black holes with quintessence and compares two methods of deriving thermodynamic laws, highlighting their differences.

Findings

Uncharged BHQ is always thermodynamically unstable.

Charged BHQ exhibits second-order phase transitions.

Different methods yield distinct thermodynamic behaviors.

Abstract

We study the thermodynamic stabilities of uncharged and charged black holes surrounded by quintessence (BHQ) by means of effective thermodynamic quantities. When the state parameter of quintessence $\omega_q$ is appropriately chosen, the structures of BHQ are something like that of black holes in de Sitter space. Constructing the effective first law of thermodynamics in two different ways, we can derive the effective thermodynamic quantities of BHQ. Especially, these effective thermodynamic quantities also satisfy Smarr-like formulae. It is found that the uncharged BHQ is always thermodynamically unstable due to negative heat capacity, while for the charged BHQ there are phase transitions of the second order. We also show that there is a great deal of difference on the thermodynamic properties and critical behaviors of BHQ between the two ways we employed.