Topological Classification of a 4D AdS Black Hole with Non-Minimal Maxwell Coupling

TL;DR

This paper classifies the thermodynamic phase structure of a 4D AdS black hole with non-minimal Maxwell coupling using topological methods, revealing how charge and coupling influence phase transitions and universality classes.

Contribution

It introduces a topological classification scheme for black hole phase structures that is independent of specific models, linking microscopic couplings to macroscopic topological classes.

Findings

Large charge black holes exhibit van der Waals-like behavior with W=1.

Small charge black holes show Hawking-Page transition with W=0.

Non-minimal coupling stabilizes the Hawking-Page universality class for charged black holes.

Abstract

We perform a topological classification of the phase structure of a four-dimensional AdS black hole with non-minimal Maxwell coupling. Critical points are treated as topological defects, allowing us to assign a winding number to each black hole branch and compute the global topological invariant W. The system exhibits a duality governed by its Maxwell charge Q: for large Q it falls into the class W = 1, displaying van der Waals-type behavior with a first-order small-large black hole transition. For small Q, it shifts to W = 0, characteristic of a Hawking-Page transition. This topological classification provides a model-independent validation of the conventional thermodynamic analysis. Crucially, we find that the non-minimal coupling lambda stabilizes the Hawking-Page universality class W=0 for black holes with non-zero charge, a phenomenon absent in the standard Reissner-Nordstrom-AdS case. This establishes a direct link between the microscopic coupling and the macroscopic topological class, demonstrating the power of topological methods in decoding thermodynamic universality across modified gravity theories.