Cooling and heating regions of Joule-Thomson expansion for AdS black holes: Einstein-Maxwell-Power-Yang-Mills and Kerr Sen black holes

TL;DR

This work extends black-hole thermodynamics by examining Joule-Thomson expansion in two AdS black-hole models: AEMPYM and AKS. It derives the Joule-Thomson coefficient and inversion curves, showing cooling/heating regions governed by the sign of $\\mu$ and identifying how model parameters ($q$, $C$, $a$, $b$) steer the ratio $T_i^{min}/T_c$, often approaching the universal value $1/2$. For AEMPYM, the ratio locks to $1/2$ at $q=1/2$ and tends to $1/2$ as Maxwell charge grows for $q>1$, with finer dependence for $1/2<q<1$ and $0<q<1/2$. For AKS, specific $(a,b)$ combinations yield $T_i^{min}/T_c\approx 1/2$, while rotation and dilaton/axion fields introduce notable deviations from Kerr-AdS behavior. Overall, the results demonstrate robust JT behavior across diverse AdS black-hole families and provide comprehensive numerical tables and plots contrasting with existing literature.

Abstract

In this paper, we study the Joule-Thomson Expansion (JTE) process for two types of black holes: AdS-Einstein-Maxwell-Power-Yang-Mills (AEMPYM) and AdS-Kerr-Sen (AKS). Our study focuses on understanding how various parameters influence the Joule-Thomson Coefficient (JTC), the inversion curve, and the ratio of minimum inversion temperature to critical temperature. For the AKS black hole, we observe that the isenthalpic curves can exhibit either cooling or heating behavior. This behavior is determined by the inversion curve, which is affected by the black hole's mass and specific parameters such as $b$ (parameter signifies the ionic charge of the black hole) and $a$ (rotation parameter). In the case of the AEMPYM black hole, our findings reveal that the ratio of minimum inversion temperature to critical temperature approaches a specific value as Maxwell's charge increases. This ratio remains constant for certain parameter values, while it varies for others. Specifically, when the parameter $q$ (real positive parameter of AEMPYM black hole) is greater than 1, the ratio is almost equal to 1/2 as Maxwell's charge (C) increases. When q equals 1/2, the ratio is exactly 1/2 for all values of (C). For values of (q) between 1/2 and 1, the ratio is close to 1/2, and for values of (q) between 0 and 1/2, the ratio decreases, moving away from 1/2. For the AKS black hole, we find that specific parameter values, such as (a = 0.00951) and (b = 0.00475 ), yield a ratio of minimum inversion temperature to a critical temperature that is approximately 1/2. This consistency across different parameter values highlights the robustness of our findings. Finally, we compare our results with those reported in the existing literature, providing a comprehensive summary in detailed tables.

Figures (8)

• Figure 1: The plot of temperature $T$ in terms of $r_+$ at $P =0.5, C=1/4, q=1/3$, and $Q=0.5$ for different values of $n$ in Fig. (\ref{['1a']}), at $P =0.5, n=2, C=0.5$, and $Q=0.5$ for different values of $q$ in Fig. (\ref{['1b']}), at $P =0.5, n=2, q=0.5$, and $Q=0.5$ for different values of $C$ in Fig. (\ref{['1c']}) and at $P =0.5, n=2, q=0.5$, and $C=0.05$ for different values of $Q$ in Fig. (\ref{['1d']}) for the AEMPYM black hole
• Figure 2: The plot of isenthalpic and inversion curves for different values of $M$. In Fig. (\ref{['2a']}) at $n =2, C=1/4, Q=0.5$, and $q=1/3$, in Fig. (\ref{['2b']}) at $n=3, q =1.5, C=0.5$, and $Q=0.5$ for the AEMPYM black hole
• Figure 3: The plot of inversion curves ($T_i-P_i$). In Fig. (\ref{['3a']}) at $n =2, C=0.5$, and $Q=1$ for different values of $q$, in Fig. (\ref{['3b']}) at $q =1.5, C=0.5$, and $Q=1$ for different values of $n$, in Fig. (\ref{['3c']}) at $n=2, q=1.5$, and $Q=1$ for different values of $C$ and in Fig. (\ref{['3d']}) at $n=2, q=1.5$, and $C=0.5$ for different values of $Q$ for the AEMPYM black hole
• Figure 4: The plot of $(\frac{T_i^{min}}{T_c})$ in terms of $C$. The solid blue line illustrated with $q=1.5, n=2$, and $Q_1=1$, solid red line denoted with $q=2, n=2$, and $Q_1=1$, dashed blue line represented with $q=1.5, n=2, Q_1=1$ and $C=0$, and dashed red line corresponds with $q=2, n=2, Q_1=1$ and $C=0$ for the AEMPYM black hole
• Figure 5: The plot of isenthalpic and inversion curves for different values of $M$. In Fig. (\ref{['5a']}) at $a=0.5$ and $b=0.5$, in Fig. (\ref{['5b']}) at $a=0.9$ and $b=0.5$, in Fig. (\ref{['5c']}) at $a=0.9$ and $b=2.5$, and in Fig. (\ref{['5d']}) at $a=0.5$ and $b=1.5$ for the AKS black hole