The Black Hole Weak Gravity Conjecture with Multiple Charges

Understand

We study the effect of higher-derivative corrections on asymptotically flat, four-dimensional, non-rotating dyonic black holes in low-energy models of gravity coupled to $N$ $U(1)$ gauge fields.

• For large extremal black holes, the leading $\mathcal{O}\left(1/Q^2\right)$ correction to the extremality bound is calculated from the most general low-energy effective action containing operators with up to four derivatives.
• Motivated by the multi-charge generalization of the Weak Gravity Conjecture, we analyze the necessary kinematic conditions for an asymptotically large extremal black hole to decay into a multi-particle state of finite charge extremal black holes.
• In the large black hole regime, we show that the convex hull condition degenerates to the requirement that a certain quartic form, constructed from the Wilson coefficients of the four-derivative effective operators, is everywhere positive.