Generalizing weak gravity conjecture

TL;DR

This paper extends the weak gravity conjecture to non-extremal black holes by deriving a generalized charge-to-mass ratio condition, linking particle properties with black hole spectra and evaporation processes.

Contribution

It introduces a generalized inequality $q/m \,\geq\, Q/M$ for non-extremal black holes, broadening the scope of the weak gravity conjecture beyond extremal cases.

Findings

Derived a new charge-to-mass ratio condition for non-extremal black holes.

Connected particle spectrum with black hole state spectrum.

Showed the generalized condition reduces to the original conjecture in extremal limit.

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.