On the extremality bound of stringy black holes

A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account. Since these corrections become more relevant in the low-mass regime, this would allow the decay of extremal black holes in terms of energy and charge conservation. Evidence in this direction has been mainly given in the context of corrections to Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass ratio of some dyonic extremal black holes explicitly embedded in the heterotic string effective theory. We find that modifications of the extremality bound depend on the solution considered, with the charge-to-mass ratio remaining unchanged or deviating positively from one. Additionally, we observe that the introduction of the higher-curvature terms increases the Wald entropy in all cases considered, whose variation does not seem to be correlated with the charge-to-mass ratio, contrary to the situation in Einstein-Maxwell theory.