Phase transition and central charge criticality of RN AdS black hole immersed in perfect fluid dark matter

Abstract

This paper delves into the thermodynamic properties of RN AdS black hole immersed in perfect fluid dark matter. We vary the Newton’s gravitational constant, cosmological constant and the perfect fluid dark matter parameter in the bulk. When studying the first law of thermodynamics for black holes, the boundary conformal field theory introduces the central charge, leading to modifications in the thermodynamic volume and chemical potential of black hole. Our analysis shows that the black hole’s free energy is affected by changes in both the central charge and the parameter of perfect fluid dark matter. The $F-T$ curve shows a swallowtail behavior when central charge is above a critical value, which means the occurrence of first-order phase transition from a small black hole to a large black hole. Additionally, we analyzed the heat capacity as a function of temperature for different PFDM parameter values to study the stability of the black hole.