Charged accelerating AdS black hole of $f(R)$ gravity and the Joule-Thomson expansion

TL;DR

This paper explores the thermodynamics and phase transitions of charged accelerating AdS black holes within $f(R)$ gravity, analyzing Joule-Thomson expansion and identifying critical points, inversion temperatures, and cooling-heating regions.

Contribution

It introduces a detailed study of phase transitions and Joule-Thomson effects for $f(R)$ gravity black holes, including derivation of inversion temperatures and analysis of cooling-heating regions.

Findings

$P-V$ criticality and van der Waals-like phase transitions occur near $T ightarrow T_c$.

Inversion temperatures and curves are derived for different black hole parameters.

The ratio of minimum inversion temperature to critical temperature is calculated.

Abstract

In this paper, the thermodynamical properties and the phase transitions of the charged accelerating anti-de Sitter (AdS) black holes are investigated in the framework of the $f(R)$ gravity. By studying the conditions for the phase transitions, it has been shown that the $P-V$ criticality and the van der Waals like phase transitions can be achieved for $ T \approx T_{c} $. The Joule-Thomson expansion effects are also examined for the charged accelerating AdS black holes of the $f(R)$ gravity. Here, we derive the inversion temperatures as well as the inversion curves. Then, we determine the position of the reverse point for different values of mass $M$ and parameter $b$ for the corresponding black hole. At this point, the Joule-Thompson coefficient is zero. So, in such case, we can say that such point is very important for the finding of cooling - heating regions. Finally, we calculate the ratio of minimum inversion temperature and critical temperature for such black hole.