Higher-order corrections to mass-charge relation of extremal black holes

TL;DR

The paper investigates whether higher-derivative corrections in quantum gravity systematically reduce the mass-to-charge ratio $M/|Q|$ of extremal black holes, making their self-interactions repulsive. It employs a perturbative four-derivative action with coefficients $c_i$ to compute corrections for a 4D Reissner-Nordström BH and, with a dilaton, for the GHS heterotic BH, deriving explicit corrected extremal relations and showing $M$ decreases relative to $Q$. In the GHS case, the mass and dilatonic charge both decrease, producing a repulsive net force between extremal states, consistent with the conjecture; a $D$-dimensional generalization reinforces the trend. The results support swampland-inspired constraints on low-energy theories coupled to gravity and motivate further proofs and explorations of Wald entropy corrections.

Abstract

We investigate the hypothesis that the higher-derivative corrections always make extremal non-supersymmetric black holes lighter than the classical bound and self-repulsive. This hypothesis was recently formulated in the context of the so-called swampland program. One of our examples involves an extremal heterotic black hole in four dimensions. We also calculate the effect of general four-derivative terms in Maxwell-Einstein theories in D dimensions. The results are consistent with the conjecture.