Criticality Quenching and Microstructure of Quintessence-AdS Black Holes

Abstract

In this work, we investigate the thermodynamic criticality and Ruppeiner geometry of four-dimensional Reissner-Nordström Anti-de Sitter (RN-AdS) black holes surrounded by quintessence, with particular emphasis on the grand canonical ensemble at fixed electric potential. We first discuss the canonical pressure-volume criticality from the fixed-potential description and show that the change of ensemble qualitatively modifies the structure of the equation of state. For the full Kiselev quintessence range and in the positive-energy sector, the fixed-potential ensemble admits no physical positive-temperature Van der Waals-type small/large black-hole critical point. This establishes that the disappearance of the conventional critical behavior is a robust consequence of the grand canonical description rather than an artifact of the particular analytically tractable choice of the quintessence state parameter. We then specialize to this tractable sector and construct the normalized Ruppeiner curvature to probe the underlying microscopic interactions. The curvature reveals an attractive-interaction regime at lower electric potential and a repulsive-interaction regime beyond a parameter-dependent crossover. Its divergence occurs along the spinodal curve, associated with the loss of local thermodynamic stability, and is distinct from that of a genuine thermodynamic critical point. Our analysis, therefore, clearly separates the ensemble-induced quenching of macroscopic criticality from the microscopic interaction crossover encoded by thermodynamic geometry.