Joule-Thomson expansion of charged dilatonic black holes

TL;DR

This paper investigates the Joule-Thomson expansion of charged dilatonic black holes in higher dimensions, analyzing how parameters like dimension and dilaton field influence the cooling-heating behavior and inversion temperature.

Contribution

It provides explicit expressions for the Joule-Thomson coefficient and explores the effects of dimension and dilaton field on inversion curves and temperature ratios, revealing new insights into black hole thermodynamics.

Findings

Inversion curve decreases with charge at low pressures and increases at high pressures.

The ratio T_min/T_c is independent of charge but depends on dilaton field and dimension.

Dilaton field enhances the T_min/T_c ratio.

Abstract

Based on the Einstein-Maxwell theory, the Joule-Thomson (J-T) expansion of charged dilatonic black holes (the solutions are neither flat nor AdS) in $(n+1)$-dimensional spacetime is studied herein. To this end, we analyze the effects of the dimension $n$ and dilaton field $\alpha$ on J-T expansion. An explicit expression for the J-T coefficient is derived, and consequently, a negative heat capacity is found to lead to a cooling process. In contrast to its effect on the dimension, the inversion curve decreases with charge $Q$ at low pressures, whereas the opposite effect is observed at high pressures. We can observe that with an increase in the dimension $n$ or parameter $\alpha$, both the pressure cut-off point and the minimum inversion temperature $T_{min}$ change. Moreover, we analyze the ratio $T_{min}/T_{c}$ numerically and discover that the ratio is independent of charge; however, it depends on the dilaton field and dimension: for $n=3$ and $\alpha=0$, the ratio is 1/2. The dilaton field is found to enhance the ratio. In addition, we identify the cooling-heating regions by investigating the inversion and isenthalpic curves, and the behavior of the minimum inversion mass $M_{min}$ indicates that this cooling-heating transition may not occur under certain special conditions.