On the extremality bound of stringy black holes

Abstract

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 chargeto-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.

α′ corrections of Reissner-Nordström black holes

“…In the context of HST, the first example of regular extremal black hole with corrections to the charge-to-mass ratio in agreement with the WGC was recently given in Ref. [8]. 11 We have also computed the corrections to the temperature and to the entropy of these black holes -see (5.10) and (6.10).…”

“…On the contrary, this claim has been disputed by the counterexample presented in Ref. [8], in which ∆S > 0 but ∆(q/M) = 0. It is interesting to ask what the situation is here, since we have a non-extremal solution at our disposal and we can perform a more detailed analysis.…”

“…In the α -corrected RN black hole, when we move towards x = 0 from the Cauchy horizon, f (x) is positive, but it always reaches a maximum and starts decreasing so that lim x→0+ f (x) = −∞. Therefore, a generic feature of the corrected black holes is that they have a third horizon inside the Cauchy horizon, 8 although it is always placed close to the region at which the curvature becomes so large that higher corrections in α can no longer be ignored.…”

“…for some numerical constant a. Notice that the charge-to-mass ratio q can differ from 1 in the extremal limit once higher-curvature interactions are incorporated [18][19][20]8], which has been connected to the weak gravity conjecture [21]. At first order in α we have…”

“…Our goal in this paper is to extend the results found in Refs. [2,3,8] to non-supersymmetric and non-extremal black holes and compute explicitly their first-order α corrections in some consistent ST effective action framework.…”