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

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 case and prove that there is no black hole bomb for D-dimensional Reissner–Nordstrom black hole under charged massive scalar perturbation and the system is superradiantly stable.

Five-dimensional Myers-Perry black holes under massive scalar perturbation: bound states and quasinormal modes

“…Compared to four-dimensional cases, the (in)stability of higher-dimensional BHs are more complicated. The higher-dimensional spherically symmetric Schwarzschild-Tangherlini spacetime and Reissner-Nordström (RN) BHs were proven to be stable when perturbed by external fields [26][27][28][29][30][31][32]. However, the black strings and p-branes constructed from the spherically symmetric BHs are generally unstable, this is known as the Gregory-Laflamme instability [33].…”

Extremal charged black holes and superradiantly unstable quasinormal modes

“…The Reissner-Nordström (RN) black hole, on the other hand, is stable under such a perturbation. The non-existence of unstable QBS's in the RN black hole was established in [8][9][10][11][12]. However, it was recently shown [7] that multicharge extremal black holes in STU supergravity [13] can suffer from such low-frequency superradiant instability as long as not all the charges of the black hole are equal.…”