Thermodynamic topology of rotating regular black hole in conformal massive gravity

In this study, we explore the thermodynamic properties of rotating regular black holes (RBH) in the context of conformal massive gravity (CMG). Our methodology involves calculating the specific heat, Gibbs free energy, and winding numbers (w) in canonical and grand canonical ensembles. These winding numbers play a crucial role in determining the thermodynamic stability of the system via topology. We derive the topological numbers of rotating regular BHs in conformal massive gravity by varying the spin (a), charge (Q), and hair parameters (lambda). Our observations reveal that lower values of the hair parameter result in a stable topological classification, while higher values lead to an unstable topological classification, which indicates the presence of a phase transition in both ensembles. This shows that these parameters play a crucial role in stability and topological classification.