Universality relation and thermodynamic topology with three-parameter entropy model

Abstract

This work investigates the extended universal relation for Reissner–Nordström–AdS (RN–AdS) black holes within the framework of a non-extensive three-parameter entropy model. This analysis provides insights into how the interplay of these parameters influences the black hole’s thermodynamic behavior and validates the universality of the relation under non-extensive entropy conditions. Then, this study delves into the topological nature of phase transitions in black hole thermodynamics. We examine the thermodynamic topology of RN–AdS black holes with parameters $\alpha$, $\beta$, and $\gamma$ within the Restricted Phase Space (RPS) thermodynamics and Bulk Boundary thermodynamics frameworks. Our findings show that the parameter $\beta$ significantly influences the number of topological charges and the classification of black holes.