Extremal rotating black holes, scalar perturbation and superradiant stability

Abstract

A (charged) rotating black hole may be unstable against a (charged) massive scalar field perturbation due to the existence of superradiance modes. The stability property depends on the parameters of the system. In this paper, the superradiant stable parameter space is studied for the four-dimensional extremal Kerr and Kerr-Newman black holes under massive and charged massive scalar perturbation. For the extremal Kerr case, it is found that when the angular frequency and proper mass of the scalar perturbation satisfy the inequality $\omega <\mu /\sqrt{3}$, the extremal Kerr black hole and scalar perturbation system is superradiantly stable. For the Kerr-Newman black hole case, when the angular frequency of the scalar perturbation satisfies $\omega <qQ/M$ and the product of the mass-to-charge ratios of the black hole and scalar perturbation satisfies $\frac{\mu }{q}\frac{M}{Q}>\frac{\sqrt{3k^2+2}}{\sqrt{k^2+2}},k=\frac{a}{M}$, the extremal Kerr-Newman black hole is superradiantly stable under charged massive scalar perturbation.

arXiv comment7 pages,4 figures,references added

References in corpus (28)

• Instability of the massive Klein-Gordon field on the Kerr spacetime
• The black hole bomb and superradiant instabilities
• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• Instability of Massive Scalar Fields in Kerr-Newman Spacetime
• Superradiant instabilities of rotating black holes in the time domain
• Floating and sinking: the imprint of massive scalars around rotating black holes
• Stability and quasinormal modes of the massive scalar field around Kerr black holes
• On the instability regime of the rotating Kerr spacetime to massive scalar perturbations
• Analytic treatment of the black-hole bomb
• Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime
• Effective stability against superradiance of Kerr black holes with synchronised hair
• The superradiant instability regime of the spinning Kerr black hole
• Massive scalar field instability in Kerr spacetime
• Ergoregion instability and echoes for braneworld black holes: Scalar, electromagnetic and gravitational perturbations
• Scalar clouds and the superradiant instability regime of Kerr-Newman black hole
• Massive Scalar Perturbations on Myers-Perry-de Sitter Black Holes with a Single Rotation
• Onset of superradiant instabilities in the composed Kerr-black-hole-mirror bomb
• On the instability for massive scalar fields in Kerr-Newman spacetime
• The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field
• Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field
• Superradiant stability of the Kerr black holes
• Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
• Algebraically special resonances of the Kerr-black-hole-mirror bomb
• Analytic study of superradiant stability of Kerr-Newman black holes under charged massive scalar perturbation
• Superradiantly stable non-extremal Reissner-Nordstrom black holes
• The spinning Kerr-black-hole-mirror bomb: A lower bound on the radius of the reflecting mirror
• Massive vector field perturbations on extremal and near-extremal static black holes
• Massive tensor field perturbations on extremal and near-extremal static black holes

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• Massive Scalar Perturbation of Extremal Rotating Braneworld Black hole: Superradiant Stability Analysis
• Dyonic Reissner-Nordstrom Black Holes and Superradiant Stability
• No black hole bomb for D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation
• Revisiting superradiant stability of Kerr-Newman black holes under a charged massive scalar
• Six-dimensional non-extremal Reissner-Nordstrom black hole, charged massive scalar perturbation and black hole bomb
• Higher-dimensional non-extremal Reissner-Nordstrom black holes, scalar perturbation and superradiance: an analytical study