Dyonic Reissner–Nordstrom black holes and superradiant stability

Abstract

Black holes immersed in magnetic fields are believed to be important systems in astrophysics. One interesting topic on these systems is their superradiant stability property. In the present paper, we analytically obtain the superradiantly stable regime for the asymptotically flat dyonic Reissner–Nordstrom black holes with charged massive scalar perturbation. The effective potential experienced by the scalar perturbation in the dyonic black hole background is obtained and analyzed. It is found that the dyonic black hole is superradiantly stable in the regime $$0<r_{-}/r_{+}<2/3$$ 0 < r - / r + < 2 / 3 , where $$r_\pm $$ r ± are the event horizons of the dyonic black hole. Compared with the purely electrically charged Reissner–Nordstrom black hole case, our result indicates that the additional coupling of the charged scalar perturbation with the magnetic filed makes the black hole and scalar perturbation system more superradiantly unstable, which provides further evidence on the instability induced by magnetic field in black hole superradiance process.

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

“…( 11) [2]. Honestly, one could not regard V (r) as a correct potential because it is negatively singular at the outer horizon and it was derived from a radial wave equation (8) without introducing the tortoise coordinate r * . We note that it was obtained just by imposing on the disappearance of Ψ ′ lm in Eq.…”

“…In this case, our interesting region of r ∈ [r + , ∞] could be mapped into the whole region of r * ∈ [−∞, ∞], which implies that the inner region of r < r + is irrelevant to analyzing the superradiant stability. Then, the radial equation (8) takes a form of the Schrödinger-type equation when setting…”

“…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.…”

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 (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.…”

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

“…For asymptotically flat black holes, the four-dimensional extremal or non-extremal Reissner-Nordstrom (RN) black hole has been proved superradiantly stable against charged massive scalar perturbation in the full parameter space of the black hole and scalar perturbation system [46][47][48][49][50][51]. The argument in the proof is that the two conditions for the possible superradiant instability of the system, (i) existence of a trapping potential well outside the black hole horizon and (ii) superradiant amplification of the trapped modes, can't be satisfied simultaneously in the RN black hole and scalar perturbation system [46,48].…”