[Paper Review] Thermodynamic of the charged accelerating AdS black hole: P-V critical and Joule-Thomson expansion

Yaling Huang, Sen Guo|arXiv (Cornell University)|Sep 20, 2020

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates the thermodynamic behavior of charged accelerating anti-de Sitter (AdS) black holes in the extended phase space, deriving their equation of state and analyzing P-V criticality and Joule-Thomson expansion. It finds that the system exhibits van der Waals-like critical behavior with identical critical exponents and a large/small black hole phase transition, while the inversion temperature increases with electric charge and decreases with acceleration parameter, though the ratio of minimum inversion temperature to critical temperature remains universally 0.5 regardless of acceleration.

ABSTRACT

In this paper, we study the thermodynamic of the charged accelerating AdS black hole in the extended phase space. Firstly, the thermodynamic quantities are derived and the state equation is obtained for this black hole. Through the investigate to the critical behavior, which shown that the charged accelerating AdS black hole as thermodynamic system is similar to the van der Waals system. The two systems share same critical exponents, and the black hole system also show that the large/small black hole phase transition. Then, we derive the inversion temperature of this black hole and plot the inversion and isenthalpic curves in the T-P plane. We find that the inversion temperature for a given pressure increases with $e$, and the acceleration parameter has the opposite effect, which the inversion curves decreases gradually with the the increases of $a$. Finally, we investigate the influence of acceleration parameter on isenthalpic curves, and obtain the ration between the minimum inversion temperature and critical temperature also is 0.5, which also means that the acceleration parameter has no effect on this universal ratio.

Motivation & Objective

• To analyze the thermodynamic properties of charged accelerating AdS black holes in the extended phase space.
• To investigate whether the system exhibits critical behavior analogous to the van der Waals system.
• To determine the Joule-Thomson expansion behavior, including inversion and isenthalpic curves.
• To examine the influence of the acceleration parameter and electric charge on thermodynamic processes.

Proposed method

• Derivation of thermodynamic quantities and equation of state for the charged accelerating AdS black hole.
• Analysis of critical behavior using the van der Waals analogy, including critical exponents and phase transition characteristics.
• Computation of inversion temperature and construction of inversion and isenthalpic curves in the T-P plane.
• Numerical investigation of the effects of electric charge $e$ and acceleration parameter $a$ on inversion and isenthalpic curves.
• Calculation of the ratio between minimum inversion temperature and critical temperature to assess universality.

Experimental results

Research questions

• RQ1 Does the charged accelerating AdS black hole exhibit P-V criticality similar to the van der Waals system?
• RQ2 How do the electric charge $e$ and acceleration parameter $a$ affect the inversion temperature and Joule-Thomson expansion?
• RQ3 What is the behavior of isenthalpic curves in the T-P plane for this black hole system?
• RQ4 Is the ratio of minimum inversion temperature to critical temperature universal, independent of the acceleration parameter?

Key findings

• The charged accelerating AdS black hole exhibits P-V criticality with critical exponents identical to those of the van der Waals system.
• The system undergoes a large/small black hole phase transition, analogous to liquid-gas transitions.
• For a given pressure, the inversion temperature increases with electric charge $e$.
• The inversion curves decrease with increasing acceleration parameter $a$, indicating a suppressive effect.
• The ratio of the minimum inversion temperature to the critical temperature is exactly 0.5, independent of the acceleration parameter, indicating universality.