Thermodynamic Topology of 4D Charged AdS Black Holes with $F^{\alpha\beta}F^{\gamma\lambda}R_{\alpha\gamma\beta\lambda}$ Coupling

TL;DR

This paper explores the thermodynamic phase transitions of a 4D charged AdS black hole with a non-minimal F^2 coupling, revealing van der Waals-like behavior and classifying its topological properties.

Contribution

It introduces a perturbative solution for the black hole with non-minimal coupling and applies topological methods to classify its thermodynamic critical points.

Findings

Exhibits van der Waals-like phase transitions.

Identifies critical points via topological analysis.

Classifies the black hole within a universal topological scheme.

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. The system displays van der Waals-like critical behavior, with a swallow-tail structure in the free energy and distinct phase branches. The topological analysis independently confirms the existence of critical points and classifies the system within the universal topological scheme for black hole thermodynamics.