Higher-Derivative Corrections to Reissner--Nordstr\"om Black Holes from Worldline QFT
In this paper we derived the corrections to the Reissner-Nordstr\"om black hole when higher-derivative $RF^2$ terms (contractions of the Riemann tensor with the Maxwell field strength squared) are added to the Einstein-Maxwell action. Such terms arise naturally in the context of effective field theories. We used wordline QFT methods to obtain the leading order post-Minkowskian corrections. We verified these results by solving the modified Einstein-Maxwell field equations in closed form, to all orders in Newton's constant $G$. We discussed the first law and computed the entropy of the perturbed black holes. When fixing the mass to that of the extremal Reissner-Nordstr\"om black hole, the entropy shift is positive if the weak gravity conjecture holds. In fact, this condition is nothing but the requirement that the spacetime with the extremal Reissner-Nordstr\"om mass possesses an outer horizon in higher-derivative gravity. This condition also rules out Drummond-Hathrell theory.