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 cases and prove that the Ddimensional 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.

Revisiting superradiant stability of Kerr–Newman black holes under a charged massive scalar

“…We note that V (r ) was obtained just by imposing on the disappearance of lm in Eq. (10). Here, it is important to point out that Eq.…”

“…Also, a similar potential was employed subsequently in deriving the conditions for superradiant stability of Kerr black holes [6]. Very recently, a similar approach was applied to testing the extremal rotating black holes under a charged massive scalar perturbation [7], dyonic Reissner-Nordström (RN) black holes under a charged massive scalar perturbation [8], higher-dimensional non-extremal RN black holes under a massive scalar perturbation [9], and D-dimensional extremal RN black holes under a charged massive scalar perturbation [10]. It may not be valid to adopt such potentials to analyzing the superradiant (in)stability of a massive scalar propagating around rotating black holes.…”

“… (Left) real part of lm (r ) as function of r ∈[10, 200] where all parameters go together with Fig.7except ω = 4 > μ = 3.85. (Right) real part of lm (r ) as function of r ∈[10, 400] where all parameters go together with Fig.3except ω = 0.05 > μ = 0.02…”

Revisiting superradiant stability of Kerr-Newman black holes under a charged massive scalar

“…Also, a similar potential was employed subsequently in deriving the conditions for superradiant stability of Kerr black holes [6]. Very recently, a similar approach was applied to testing the extremal rotating black holes under a charged massive scalar perturbation [7], dyonic Reissner-Nordström black holes under a charged massive scalar perturbation [8], higherdimensional non-extremal Reissner-Nordström black holes under a massive scalar perturbation [9], and D-dimensional extremal Reissner-Nordström black holes under a charged massive scalar perturbation [10]. It may not be valid to adopt such potentials to analyzing the superradiant (in)stability of a massive scalar propagating around rotating black holes.…”

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]. However, it was recently shown [7] that multicharge extremal black holes in STU supergravity [12] can suffer from such low-frequency superradiant instability as long as not all the charges of the black hole are equal (When all the charges are equal, the black hole becomes the RN black hole.…”