Eur. Phys. J. C (2026) 86: 581
https://doi.org/10.1140/epjc/s10052-026-15747-4

Regular Article - Theoretical Physics

Thermodynamic topology of 4D charged AdS black holes with $F^{\alpha \beta }{F}^{\gamma \lambda }{R}_{\alpha \gamma \beta \lambda }$ coupling

Department of Physics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran

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Received: 18 February 2026
Accepted: 23 April 2026
Published online: 27 May 2026

Abstract

We investigate the thermodynamic phase transitions of a four-dimensional charged anti-de Sitter black hole endowed with a non-minimal coupling of the form $F^{\alpha \beta }{F}^{\gamma \lambda }{R}_{\alpha \gamma \beta \lambda }$. Using perturbative methods, we derive a consistent black hole solution and analyze its thermodynamics through both conventional equilibrium techniques and a topological defect classification approach. In the canonical ensemble, the system displays van der Waals-like critical behavior, with a swallow-tail structure in the free energy and distinct phase branches. In the grand canonical ensemble, by contrast, the system exhibits a Hawking–Page-like transition, characterized by a single divergence in the heat capacity and the absence of a swallowtail. The topological analysis independently confirms both types of critical behavior: it classifies the canonical ensemble within class $W^{1+}$ and the grand canonical ensemble within class $W^{0-}$. Our results demonstrate that the non-minimal coupling preserves the universal topological classification while allowing ensemble choice to fundamentally alter the phase structure.