Abstract
Previously, the Maxwell equal-area law has been used to discuss the conditions satisfied by the phase transition of charged AdS black holes with cloud of string and quintessence, and it was concluded that black holes have phase transition similar to that of vdW system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On the basis of this result, we study the relation between the latent heat of the phase transition and the parameter of dark energy, and use the Landau continuous phase transition theory to discuss the critical phenomenon of the black hole with quintessence and give the critical exponent. By introducing the number density of the black hole molecules, some properties of the microstructure of black holes are studied in terms of a phase transition. It is found that the electric charge of the black hole and the normalization parameter related to the density of quintessence field play a key role in the phase transition. By constructing the binary fluid model of the black hole molecules, we also discuss the microstructure of charged AdS black holes with a cloud of strings and quintessence.
Highlights
Where lp is the Planck length, lp = h G/c3
The microscopic behavior of the thermal stable AdS black hole was studied completely from the thermodynamic point of view by Ruppeiner’s thermodynamic geometry method, combining the “black hole molecule” hypothesis and the concept of microscopic particle number density in [5–8], and one has given a natural explanation for the microscopic behavior of the black hole
In the case of a van der Waals (vdW) system, the microstructure of the system changes as the fluid undergoes a liquid–gas phase transition, and the physical properties of the system change [1–3]. It is well known from the study of the black hole system that when the system meets the requirement of thermodynamic equilibrium stability in isothermal or isobaric process, the P–V curve or T –S curve describing the change of the system is discontinuous, and the system has the latent heat of the phase transition when it crosses the two-phase coexistence curve
Summary
The cosmological constant is interpreted as the pressure in the thermodynamic system [9–59] With these issues, the thermodynamic characteristics and critical phenomena of AdS and dS black holes are studied, and the first-order and second-order phase transitions of RN-AdS black holes are obtained [8,9,60]. The microscopic interpretation of the black hole phase transition and the critical exponential thermodynamic geometry method, as a unique perspective, played an important role in the study of the black hole phase transition. 4, we analyze the influence of each parameter on the latent heat of the phase transition when the first-order phase transition occurred in charged AdSQ black hole.
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