Dunkl-Corrected Deformation of RN-AdS Black Hole Thermodynamics

TL;DR

This paper introduces a Dunkl-deformed four-dimensional Einstein–Maxwell framework to produce a new class of charged AdS black holes, deriving the metric function with Dunkl parameters A and B. It analyzes thermodynamic properties, including temperature, entropy, and heat capacity, and studies stability. It establishes P–v criticality, a universal ratio P_c v_c / T_c dependent on A, and investigates Joule–Thomson expansion and Gibbs energy-driven phase transitions, recovering RN–AdS in the undeformed limit. The results link discrete reflection symmetries in spacetime to black hole thermodynamics, with Van der Waals–like behavior and potential avenues for rotating solutions and data-constrained deformations.

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.

Figures (5)

• Figure 1: Effect of the charge parameter $Q$ and the Dunkl parameter $A$ on the metric function $f(r)$ by considering $B=1$.
• Figure 2: Charge parameter effect $Q$ on the temperature by taking $B=1$ for two different values of $A$.
• Figure 3: Effect of the charge parameter $Q$ on the heat capacity by taking $B=1$ for two different values of $A$
• Figure 4: Pressure in terms of $v$ for different values of $T$ and $A$ with $B=1$.
• Figure 5: Gibbs free energy in terms of the temperature for different values of $P$ and $Q$, with $B=1$.