Dunkl-Corrected Deformation of RN-AdS Black Hole Thermodynamics

TL;DR

This paper introduces Dunkl derivatives into four-dimensional spacetime to derive new charged black hole solutions, analyzing their thermodynamics, stability, and phase transitions, revealing universal ratios and Van der Waals-like behaviors.

Contribution

The work develops a novel class of charged black holes using Dunkl derivatives, extending Einstein equations and thermodynamics analysis with new parameters.

Findings

Derived charged Dunkl black hole solutions.

Identified universal critical ratios independent of charge.

Revealed Van der Waals-like phase behavior in the thermodynamics.

Abstract

In this work, we derive a new class of charged black holes by introducing Dunkl derivatives in the four dimensional spacetime. To construct such solutions, we first compute the Ricci tensor and the Ricci scalar using the Christoffel symbols. Substituting them into the modified Einstein field equations via extended Dunkl derivations, we obtain the metric function of charged Dunkl black holes. Next, we investigate the charge effect on the corresponding thermodynamical properties by computing the associated quantities. To study the thermal stability, we calculate the heat capacity. After that, we approach the P-v criticality behaviors by determining the critical pressure Pc, the critical temperature Tc and the critical specific volume vc in terms of Q and two parameters A and B carrying data on the Dunkl reflections. Precisely, we show that the ratio Pcvc Tc is a universal number with respect to the charge Q and B parameters. Taking a zero limit of A, we recover the Van der Waals fluid behaviors. For Joule-Thomson expansion effects for such charged black holes, we reveal certain similarities and the differences with Van der Waals fluids. Finally, we discuss the phase transitions via the Gibbs free energy computations.