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

TL;DR

This paper proves analytically that D-dimensional extremal Reissner-Nordstrom black holes are stable against charged massive scalar perturbations, extending previous numerical results and confirming the absence of superradiant instabilities.

Contribution

The paper applies a new analytical method to prove superradiant stability of D-dimensional extremal Reissner-Nordstrom black holes, generalizing prior results to arbitrary dimensions.

Findings

D-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable.

The analytical proof confirms previous numerical observations.

Stability holds under charged massive scalar perturbations in all considered dimensions.

Abstract

The superradiant stability of asymptotically flat D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is analytically studied. Recently, an analytical method has been proposed by the author and used to prove that five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable under charged massive scalar perturbation. We apply this analytical method in the D-dimensional extremal Reissner-Nordstrom black hole cases and prove that the D-dimensional Reissner-Nordstrom black holes are all superradiantly stable under charged massive scalar perturbation. Our result is consistent with the previous numerical observation in the literature and provides a rigorous analytical proof.