Higher-Derivative Corrections to Extremal Black Holes and the Weak Gravity Conjecture

Weak Gravity Conjecture (WGC) arguments suggest that higher order derivative corrections to the black hole horizon can make the extremal black hole configurations violate the naive extremality bound of charge-to-mass ratio. These corrections could change black holes mechanics allowing them to decay through a splitting process. We analyze such a possibility considering the effects of higher derivative corrections to the entropy law. We also show in the framework of 4 derivative Einstein--Maxwell theory that the mild form of the WGC together with the Electric--Magnetic duality implies the same conditions as unitarity, locality and positivity of the scattering amplitudes of the same theory.