Quantum gravitational corrections to the geometry of charged AdS black holes

We consider a modified gravity by higher-derivative gravity coupled with non-local terms and Maxwell electrodynamics. By employing the effective field theory framework for quantum gravity, we compute quantum corrections to the entropy of charged AdS black holes, focusing on second-order curvature terms. By incorporating scale-dependent coefficients, we establish that the Wald entropy is renormalization group (RG) invariant, confirming the robustness of the framework. Additionally, quantum corrections to thermodynamic quantities-temperature, pressure, specific heat, and Helmholtz free energy-are derived, all satisfying the first-law of thermodynamics. Specific heat and Helmholtz free energy also exhibit RG invariance, demonstrating stability under scale transformations. These findings highlight the effectiveness of the approach in describing quantum modifications to charged AdS black hole thermodynamics, offering insights into the interplay between quantum gravity and black hole physics.