Generalizing weak gravity conjecture

The weak gravity conjecture implies the necessary existence of particles with charge-to-mass ratio q/m≥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 nonextremal black holes, we solve the problem of a charged shell of mass and charge (m, q) from a black hole with mass (M, Q). We find a more general condition q/m≥Q/M, which obviously reduces to the weak gravity conjecture in the extremal limit; however, it relaxes the condition for complete evaporation of nonextremal black holes. This condition also allows us to directly relate the particle content of the theory with the spectrum of black hole states.