Quantum gravitational corrections to Reissner-Nordström black hole thermodynamics and their implications for the weak gravity conjecture*

Abstract In this paper, we investigate the quantum gravitational corrections to the thermodynamical quantities of Reissner-Nordström black holes within the framework of effective field theory. The effective action originates from integrating out massless particles, including gravitons, at the one-loop level. We perform a complete thermodynamic analysis for both non-extremal and extremal black holes and are mainly concerned with the shift in the charge-to-mass ratio , which plays an important role in analyzing the weak gravity conjecture. For non-extremal black holes, we identify a relationship between the shift in the charge-to-mass ratio and the thermodynamic stability of the black holes. For extremal black holes, we show that quantum gravity effects naturally lead to the super-extremality of charged black holes.