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

Considering the variable cosmological constant in the extended phase space has a significant background in the black hole physics. It has been shown that the thermodynamic behavior of charged anti-de Sitter 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 nonextended 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 of 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.

Automated summary

The study explores the influence of the cosmological constant on the thermodynamic behavior in black hole physics, revealing similarities between black hole phase transitions and liquid/gas phase transitions in van der Waals fluid. Additionally, the research delves into related behaviors in the non-extended phase space.