Thermodynamic topology of AdS black holes with $F^{\alpha \beta }{F}^{\gamma \lambda }{R}_{\alpha \gamma }{R}_{\beta \lambda }$ coupling in the grand canonical ensemble

Abstract

We investigate the thermodynamic and topological phase structure of charged AdS black holes with a nonminimal gauge--curvature coupling in the grand canonical ensemble. In the minimal-coupling limit $\epsilon =0$, the system exhibits only Hawking--Page-like behavior and does not possess van der Waals criticality. Working perturbatively in the nonminimal coupling, we find that the $\epsilon \ne 0$ interaction generates a rich phase structure as the electric potential is varied, including several distinct regimes of critical behavior, a double-critical region, and a regime where conventional criticality disappears. We complement the conventional thermodynamic analysis with a topological description based on the winding number of the thermodynamic vector field. The resulting $r_h$--$\tau$ diagrams reveal that the ordering and morphology of the black-hole branches depend sensitively on both the pressure and the off-shell inverse temperature, with monotonic, disconnected, S-shaped, and cusp-like structures appearing in different parameter ranges. Remarkably, these substantial rearrangements of the solution branches can occur without changing the global winding number. In particular, the system remains in the $W=+1$ topological class beyond the range of conventional criticality, before eventually entering a $W=0$ sector. Our results demonstrate that thermodynamic topology provides complementary global information that is not captured by conventional local criticality criteria alone.

arXiv commentIn Version 2, we made minor changes to the abstract and conclusion of the manuscript. We have also added several new references. 84 figures