Weak Gravity Conjecture and Black Holes in $N = 2$ Supergravity

Abstract

In a previous paper \cite{Cottrell:2016bty}, we used the entropy function formalism to argue that loops of charged particles can give unexpected contributions to the entropy of extremal black holes. Here, we show that similar results hold for loops of BPS particles in $\mathcal{N}=2$ supergravity, potentially connecting these results to familiar string setups. However, we will argue that string theory avoids these corrections altogether with the help of the Weak Gravity Conjecture. Finally, we discuss the relationship between these results and the semi-classical analysis of Antonov \cite{antonov,1989ApJS}, who showed that sub-extremal particles suffer a `gravo-thermal catastrophe' in the Newtonian limit.