Generalizing weak gravity conjecture

Abstract

The weak gravity conjecture implies the necessary existence of particles with charge-to-mass ratio $q/m \geq 1$ so that the extremal charged black hole can completely evaporate without leaving a dangerous stable extremal remnant while simultaneously not revealing a naked singularity along the way. In other words, this inequality ensures that the charge is emitted faster than the mass of a black hole, which is in turn coincidentally consistent with the fact that gravitational interaction for such parties is weaker than electromagnetic. To extend this argument to non-extremal black holes, we solve the problem of a charged shell of mass and charge ($m,q$) from a black hole with ($M,Q$). We find a more general condition $q/m \geq Q/M$, which obviously reduces to the weak gravity conjecture in the extremal limit, however it relaxes the condition for complete evaporation of non-extremal black holes. This condition also allows us to directly relate the particle content of the theory with the spectrum of black hole states.