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, we study 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 $M>\sqrt{Q^2+α}$ by combining a non-perturbative, quantum-gravity-inspired exponential correction to the entropy (quantified by $η$) with information-geometric diagnostics. Working in a canonical ensemble (fixed $Q$) paradigm, we identify thermodynamic stability regions and phase-transition-like features as the black hole size tends toward extremality due to Hawking evaporation. We then construct the Ruppeiner metric on the $(M,Q)$ state space and evaluate the associated thermodynamic curvature 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.

Figures (6)

• Figure 1: Impact of $\alpha$ on (a) the metric function $f(r)$, where it indicates finiteness of the metric coefficient at $r\rightarrow 0$ compared to Einstein gravity ($\alpha=0$) , and (b) horizon radius $r_{+}$ depicting how $\alpha$ shrinks the black hole.
• Figure 2: Black hole temperature $T_{\rm BH}$ vs the mass $M$. The GB coupling $\alpha$ parameter tends to make the black hole colder on smaller scales, mimicking the role of charge in RN geometry.
• Figure 3: Variation of black hole entropy with respect to (a) exponential parameter $\eta$, and (b) GB coupling $\alpha$. Exponential contributions become dominant on quantum scales compared to Bekenstein-Hawking term.
• Figure 4: Heat capacity $C_{Q}$ as a function of black hole mass $M$ for $Q=1$ and GB coupling (a) $\alpha=0.1$ and (b) $\alpha=0.2$. The second zero of $C_{Q}$ occurs whenever $M=\sqrt{Q^2+\alpha}$.
• Figure 5: (a) Impact of quantum corrections on the Helmholtz free energy of the black hole, and (b) Quantum work as a function of the black hole size, where it is significant for microscopic geometries and negligible for larger scales.