Superradiant instability of extremal brane-world Reissner-Nordstr\"{o}m black holes to charged scalar perturbations

We examine the stability of extremal braneworld Reissner-Nordstr\"{o}m black holes under massive charged scalar perturbations. We show that similar to the four-dimensional case, the superradiant amplification can occur in braneworld charged holes. More interestingly we find that when the spacetime dimension is higher than four, a trapping potential well can emerge outside the braneworld black hole. This potential well is the extra dimensional effect and does not exist in four dimensions. It triggers the superradiant instability of the extremal braneworld charged holes.