No black hole bomb for $D$-dimensional non-extremal Reissner-Nordstrom black holes against charged massive scalar perturbation

The superradiant stability of asymptotically flat $D$-dimensional non-extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is analytically studied. In previous works, it proved that there are no black hole bombs for five and six-dimensional non-extremal Reissner-Nordstrom black holes against charged massive scalar perturbation. In this work, we extend the previous discussions to the $D$-dimensional case ($D\ge 7$) and find that the same conclusion holds in arbitrary higher dimensional case.