Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space

TL;DR

This paper demonstrates that charged AdS black holes with quintessence exhibit van der Waals-like phase transitions and critical behavior even in a non-extended phase space by considering the normalization factor as a thermodynamic variable.

Contribution

It introduces a new thermodynamic framework for charged AdS black holes with quintessence, revealing phase transition behavior without varying the cosmological constant.

Findings

Black holes show first-order small/large phase transition similar to liquid/gas.

Critical exponents match those of the van der Waals system.

Shadow radius correlates with phase transitions and critical phenomena.

Abstract

Considering the variable cosmological constant in the extended phase space has a significant background in the black hole physics. It was shown that the thermodynamic behavior of charged AdS black hole surrounded by the quintessence in the extended phase space is similar to the van der Waals fluid. In this paper, we indicate that such a black hole admits the same criticality and van der Waals like behavior in the non-extended phase space. In other words, we keep the cosmological constant as a fixed parameter, and instead, we consider the normalization factor as a thermodynamic variable. We show that there is a first-order small/large black hole phase transition which is analogous to the liquid/gas phase transition in fluids. We introduce a new picture of the equation of state and then we calculate the corresponding critical quantities. Moreover, we obtain the critical exponents and show that they are the same values as the van der Waals system. Finally, we study the photon sphere and the shadow observed by a distant observer and investigate how the shadow radius may be affected by the variation of black hole parameters. We also investigate the relations between shadow radius and phase transitions and calculate the critical shadow radius where the black hole undergoes a second-order phase transition.