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

TL;DR

This work investigates quantum gravitational corrections to Reissner–Nordström black hole thermodynamics using a one-loop, nonlocal effective action that arises from integrating out massless fields. The leading corrections are encoded in nonlocal form factors such as $R \ln(\Box/\mu_*^2) R$, with coefficients $\beta$ and $\gamma$ determined by the low-energy spectrum; the authors compute the corrected Euclidean action, free energy, and thermodynamic quantities, obtaining explicit expressions for the corrected mass $M$, entropy $S$, and electrostatic potential $\Phi$. They show that for non-extremal RN black holes within the thermodynamically stable window $q \le \bar{r}_h < \sqrt{3}\,q$, the mass decreases with the EFT parameter $\epsilon$, increasing the charge-to-mass ratio $q/M$, while at extremality the corrections yield $M_{\text{ext}}$ that decrease with $\epsilon$, leading to $q/M>1$ and supporting the weak gravity conjecture. The analysis also links logarithmic entropy corrections to the super-extremality required by the WGC, highlighting a deep connection between quantum gravity loop effects and black hole thermodynamics in a model-independent, EFT framework, albeit with UV sensitivity through $\mu_*$. Overall, the results reinforce the view that quantum gravity loop effects can favor decay channels for extremal black holes and provide a robust IR signature compatible with the WGC.

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 about the shift in the charge-to-mass ratio $q/M$ that plays an important role in analyzing the weak gravity conjuecture. 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 $q/M>1$ of charged black holes.