2026/06/20 by Mehdi Sadeghi, Faramarz Rahmani
#hep-th
The conventional and topological phase transitions of a four-dimensional asymptotically AdS black hole with a non-minimal coupling term FαβFγλRαγRβλ are investigated. Using a perturbative approach to first order in the coupling ε, the thermodynamic quantities are derived and the first law and Smarr relation are verified. Intriguingly, while the ε= 0 limit yields the standard Reissner--Nordström--AdS black hole belonging to the W1+ topological class (W = +1), switching on the non-minimal coupling fundamentally transforms the topology to the W0- class (W = 0). This transition occurs while the van der Waals-type first-order phase transition survives in the intermediate region, embedded within the overall Hawking--Page pattern, rendering the system a hybrid black hole thermodynamic system. The coupling ε thus acts as a topological deformation parameter that alters the universal classification of the system, despite the perturbative nature of the solution.