Abstract <p> 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P\)</EquationSource> </InlineEquation>–<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(v\)</EquationSource> </InlineEquation> criticality behaviors by determining the critical pressure <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(P_{\mathrm c}\)</EquationSource> </InlineEquation>, the critical temperature <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(T_{\mathrm c}\)</EquationSource> </InlineEquation> and the critical specific volume <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(v_{\mathrm c}\)</EquationSource> </InlineEquation> in terms of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(Q\)</EquationSource> </InlineEquation> and two parameters <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation> characterizing the Dunkl reflections. Precisely, we show that the ratio <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(P_{\mathrm c}v_{\mathrm c}/T_{\mathrm c}\)</EquationSource> </InlineEquation> is a universal number with respect to the charge <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(Q\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation> parameters. Taking a zero limit of <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation>, 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. </p>

Dunkl-corrected deformation of RN–AdS black hole thermodynamics

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发表日期：

2026年4月23日

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M. Jemri

摘要

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 \(P_{\mathrm c}\) , the critical temperature \(T_{\mathrm c}\) and the critical specific volume \(v_{\mathrm c}\) in terms of \(Q\) and two parameters \(A\) and \(B\) characterizing the Dunkl reflections. Precisely, we show that the ratio \(P_{\mathrm c}v_{\mathrm c}/T_{\mathrm c}\) 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.