Short-distance thermal phase structure of charged black holes in 4D Einstein-Gauss-Bonnet gravity

Abstract

Glavan and Lin's proposal of an effective four-dimensional Einstein--Gauss--Bonnet (4D-EGB) gravity framework yields predictions that differ from general relativity in some regimes. A range of black hole studies have offered insights into the dynamical and phenomenological aspects of this effective theory of gravity. In this work, the thermodynamics of a charged 4D-EGB black hole with Gauss--Bonnet (GB) coupling $α$, characterized by mass $M$ and charge $Q$ in the non-extremal regime $M>\sqrt{Q^2+α}$ is investigated by combining a non-perturbative, quantum-gravity-inspired exponential correction to the entropy (quantified by $η$) with information-geometric diagnostics. Within a canonical ensemble (fixed $Q$) paradigm, thermodynamic stability regions and phase-transition-like features are identified as the black hole size tends toward extremality due to Hawking evaporation. The Ruppeiner metric is then constructed on the $(M,Q)$ state space and the associated thermodynamic curvature is evaluated to characterize the effective interaction signatures and its relation to critical behavior. In addition, an effective quantum-work quantity, defined from the free-energy landscape using Jarzynski equality, is evaluated as an additional probe of short-distance, near-extremal behavior. The results indicate that departures from the general-relativistic behavior are negligible for large black holes but can become relevant at small horizon scales. Specifically, on short-distance scales, the combined influence of $α$ and $η$ can modify stability of the extremal black hole geometry and remnants within this thermodynamic model.