Thermodynamic curvature in phase transitions of the Hayward-AdS black hole

Abstract We investigate P – V criticality, with a focus on Ruppeiner geometry, in the extended phase space of the Hayward-anti de Sitter (AdS) black hole. Through thermodynamic analysis, we confirm that the Hayward-AdS black hole undergoes P – V phase transitions and exhibits well-defined critical phenomena in the vicinity of its critical point. These behaviors are characterized by four critical exponents that typically obey the scaling laws predicted by mean-field theory, indicating a thermodynamic framework consistent with that of classical phase transition systems (e.g., van der Waals fluids). Furthermore, we employ Ruppeiner geometry to probe the thermodynamic fluctuations of the Hayward-AdS black hole. By evaluating the thermodynamic curvature, we gain direct insights into the nature of interactions among the microscopic constituents of the Hayward-AdS black hole.