| Abstract : | Thermodynamic geodesics of 4D asymptotically anti-de Sitter black holes in the context of Quevedo type II geothermodynamic (GTD) metric is studied. We construct Quevedo type II metric for four different black holes: 4D KN-AdS, K-AdS, RN-AdS, and Dyonic AdS black holes in various ensembles. For K-AdS and RN-AdS black holes we work in canonical as well as grand canonical ensembles. For KN-AdS and Dyonic AdS black holes, in addition to these two ensembles we also consider a mixed canonical ensemble. For each case, the corresponding geodesic equations numerically solved and we analyze their behavior near the spinodal curves. These spinodal curves which separate the positive specific heat region from the negative specific heat region can be treated as the boundary between two black hole phases in the thermodynamic parameter space. We find that, in all the cases under consideration, geodesics are confined to a single phase and exhibit either turning behavior or incompleteness near the spinodal curve. Our results indicate a universality in the behavior of Quevedo type II geodesics for KN-AdS, K-AdS, RN-AdS, and Dyonic AdS black holes in different ensembles. |
