Overcharging higher-dimensional black holes with point particles

We investigate the possibility of overcharging spherically symmetric black holes in spacetime dimensions $D>4$ by the capture of a charged particle. We generalize Wald's classic result that extremal black holes cannot be overcharged. For nearly extremal black holes, we also generalize Hubeny's scenario by showing that overcharging is possible in a small region of parameter space. We check how D affects the overcharging parameter space and find that this appears to shrink in the large-D limit, which suggests that overcharging becomes increasingly difficult in higher dimensions.