Abstract
We revisit the superradiant stability of five and six-dimensional extremal Reissner–Nordstrom black holes under charged massive scalar perturbation with a new analytical method. In each case, it is analytically proved that the effective potential experienced by the scalar perturbation has only one maximum outside the black hole horizon and no potential well exists for the superradiance modes. So the five and six-dimensional extremal Reissner–Nordstrom black holes are superradiantly stable. The new method we developed is based on the Descartes’ rule of signs for the polynomial equations. Our result provides a complementary support of previous studies on the stability of higher dimensional extremal Reissner–Nordstrom black holes based on numerical methods.
Highlights
Superradiance is an interesting phenomenon in black hole physics [1–5]
When a charged bosonic wave is impinging upon a charged rotating black hole, the wave is amplified by the black hole if the wave frequency ω obeys ω < n H +e H, (1)
Where e and n are the charge and azimuthal number of the bosonic wave mode, H is the angular velocity of the black hole horizon and H is the electromagnetic potential of the black hole horizon
Summary
Superradiance is an interesting phenomenon in black hole physics [1–5]. When a charged bosonic wave is impinging upon a charged rotating black hole, the wave is amplified by the black hole if the wave frequency ω obeys ω < n H +e H,. Where e and n are the charge and azimuthal number of the bosonic wave mode, H is the angular velocity of the black hole horizon and H is the electromagnetic potential of the black hole horizon This superradiant scattering was studied long time ago [6–12], and has broad applications in various areas of physics(for a comprehensive review, see [4]). Among the study of superradiant (in)stability of black holes, an interesting result is that the four-dimensional extremal and non-extremal Reissner–Nordstrom (RN) black holes have been proved to be superradiantly stable against charged massive scalar perturbation in the full parameter space of the black-hole-scalar-perturbation system [42–45]. We will develop a analytical method and prove the superradiant stability of five and six-dimensional extremal RN black holes under charged massive scalar perturbation.
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