Thermodynamic phase description of charged 4D Gauss-Bonnet black holes in quantum regime (2406.05820v3)

Abstract: Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] ave argued for a 4D theory of Gauss-Bonnet (GB)gravity. This model predicts significant contributions of the GB coupling parameter $\alpha$ to gravitational dynamics, while circumventing the Lovelock theorem and avoiding Ostrogradsky instability. As a powerful competitor to general relativity (GR), the model has been examined on various phenomenological grounds. Here, we employ a technique from information geometry to analyze the thermodynamic phase structure of a charged black hole with a quantum gravity-inspired entropy relation in this novel modified gravity theory scenario. Based on the sign and magnitude of thermodynamic curvature, we demonstrate that while the theory does not significantly impact larger black holes, it may lead to multiple phase transitions and accelerate the formation of black hole remnants at short-distance scales compared to GR. Our analysis focuses solely on the non-extremal geometry case where $M>\sqrt{Q^2+\alpha}$, with $M$ and $Q$ representing the mass and charge of the black hole, respectively. Moreover, since black hole thermodynamics can be effectively analyzed through quantum thermodynamics at microscopic scales, we compute the quantum work associated with the evaporation process of a black hole and demonstrate its intricate behavior in smaller geometric regimes. We believe that these results may offer insights for testing the phenomenological consistency of the theory as a potential alternative to the standard Einstein paradigm.