Thermodynamic phase structure and topological charge of Hayward-AdS black holes under phase space constraints

Abstract: We investigate the thermodynamic behavior of the Hayward-AdS black hole and compare it with its singular counterpart from which it can be constructed through the imposition of an additional constraint. The singular black hole displays a rich phase structure, including reentrant phase transitions reminiscent of those observed in higher-dimensional Kerr-AdS spacetimes. After the constraint is imposed, the resulting Hayward-AdS black hole continues to exhibit Van der Waals-type $P-V$ criticality. However, its Gibbs free energy profile differs qualitatively from that of standard RN-AdS black holes. In addition, we extend the analysis by employing thermodynamic topology to characterize the global structure of the phase space. We find that the topological charge of the singular black hole is $-1$, whereas that of the Hayward-AdS black hole becomes $+1$. This change of topological charge indicates that the constraint not only regularizes the geometry but also induces a qualitative transformation in the thermodynamic configuration space.