Alfv\'enic superradiance for a monopole magnetosphere around a Kerr black hole
2021
We explore superradiance for Alfv\'en waves (Alfv\'enic superradiance) in an
axisymmetric rotating magnetosphere of a Kerr black hole within the force-free
approximation. On the equatorial plane of the Kerr spacetime, the Alfv\'en wave
equation is reduced to a one-dimensional Schr\"{o}dinger-type equation by
separating variables of the wave function and introducing a tortoise coordinate
mapping the inner and outer light surfaces to $-\infty$ and $+\infty$,
respectively, and we investigate a wave scattering problem for Alfv\'en waves.
An analysis of the asymptotic solutions of the wave equation and the
conservation of the Wronskian give the superradiant condition for Alfv\'en
waves, and it will be shown that the condition coincides with that for the
Blandford-Znajek process. This means that when Alfv\'enic superradiance occurs,
the Blandford-Znajek process also occurs in the force-free magnetosphere. Then,
we evaluate the reflection rate of Alfv\'en waves numerically and confirm that
Alfv\'enic superradiance is indeed possible in the Kerr spacetime. Moreover, we
will discuss a resonant scattering of Alfv\'en waves, which is related to a
"quasinormal mode" of the magnetosphere.
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