[Paper Review] Cooling-heating phase transition for 4D AdS Bardeen Gauss-Bonnet Black Hole

Mohammad Farsam, Emad Yaraie+2 more|arXiv (Cornell University)|Oct 8, 2020

Black Holes and Theoretical Physics44 references4 citations

TL;DR

This paper investigates the Joule-Thomson expansion and cooling-heating phase transition in 4D asymptotically AdS Bardeen Gauss-Bonnet black holes. By analyzing the Joule-Thomson coefficient and its zero-crossing, the study reveals that variations in mass, magnetic charge, and Gauss-Bonnet coupling induce inversion temperatures, signaling a phase transition between cooling and heating regimes, analogous to conventional thermodynamic systems.

ABSTRACT

In this letter we study thermodynamics of 4D AdS Bardeen Gauss-Bonnet (BGB) black hole. We show it can be involved in the process of the Joule-Thomson expansion. This is done by studying its inversion temperatures. Same as ordinary thermodynamics systems this black hole predicts cooling/heating phase transition if Joule-Thomson coefficient vanishes. Here we investigate effects of the black hole characteristics such as the magnetic charge, the mass and the GB coupling constant variations on the inversion temperature and the phase transition.

Motivation & Objective

• To explore thermodynamic behavior of 4D AdS Bardeen Gauss-Bonnet black holes under Joule-Thomson expansion.
• To determine conditions under which cooling or heating occurs during expansion.
• To analyze the role of black hole parameters—mass, magnetic charge, and Gauss-Bonnet coupling—on inversion temperature and phase transition.
• To establish a thermodynamic analogy between black hole systems and conventional matter in Joule-Thomson processes.

Proposed method

• Analysis of the Joule-Thomson coefficient to identify regions of cooling and heating during expansion.
• Derivation and evaluation of inversion temperature as the point where the Joule-Thomson coefficient vanishes.
• Investigation of the dependence of inversion temperature on mass, magnetic charge, and Gauss-Bonnet coupling constant.
• Use of thermodynamic relations specific to Gauss-Bonnet gravity in anti-de Sitter spacetime.
• Numerical and analytical study of phase transition boundaries in parameter space.

Experimental results

Research questions

• RQ1 At what conditions does the Joule-Thomson coefficient of the 4D AdS Bardeen Gauss-Bonnet black hole vanish, indicating a phase transition?
• RQ2 How do variations in the black hole's mass affect the inversion temperature and cooling-heating transition?
• RQ3 What is the influence of the magnetic charge on the inversion temperature and phase behavior?
• RQ4 How does the Gauss-Bonnet coupling constant modulate the thermodynamic transition characteristics?
• RQ5 Can the black hole exhibit a phase transition analogous to those in ordinary thermodynamic systems?

Key findings

• The 4D AdS Bardeen Gauss-Bonnet black hole exhibits a cooling-heating phase transition when the Joule-Thomson coefficient crosses zero, indicating a thermodynamic phase boundary.
• Inversion temperature increases with higher mass and magnetic charge, suggesting enhanced cooling potential at elevated values.
• The Gauss-Bonnet coupling constant modulates the inversion temperature, with non-trivial effects on the phase transition regime.
• The system displays behavior analogous to conventional thermodynamic systems, including distinct cooling and heating phases.
• The phase transition is sensitive to all three key parameters: mass, magnetic charge, and Gauss-Bonnet coupling, indicating tunable thermodynamic response.