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 P ₂, the critical temperature T ₂ and the critical specific volume v ₂ in terms of Q and two parameters A and B characterizing the Dunkl reflections. Precisely, we show that the ratio P ₂v ₂/T ₂ 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.
M. Jemri (Wed,) studied this question.