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

TL;DR

This paper investigates the thermodynamics and phase structure of charged black holes in a novel 4D Einstein-Gauss-Bonnet gravity framework, revealing how quantum corrections and short-distance effects influence stability and critical behavior.

Contribution

It introduces a combined analysis of quantum-inspired entropy corrections and information geometry to study black hole thermodynamics in 4D-EGB gravity, highlighting effects near extremality.

Findings

Large black holes show negligible deviations from general relativity.

Short-distance scales exhibit modified stability and phase behavior due to Gauss-Bonnet and quantum effects.

Thermodynamic curvature relates to critical phenomena and effective interactions.

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 $\alpha$, characterized by mass $M$ and charge $Q$ in the non-extremal regime $M>\sqrt{Q^2+\alpha}$ is investigated by combining a non-perturbative, quantum-gravity-inspired exponential correction to the entropy (quantified by $\eta$) 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 $\alpha$ and $\eta$ can modify stability of the extremal black hole geometry and remnants within this thermodynamic model.