Alfv\'enic superradiance for a monopole magnetosphere around a Kerr black hole

TL;DR

This paper investigates Alfvén wave superradiance in Kerr black hole magnetospheres, demonstrating conditions for superradiance, its relation to the Blandford-Znajek process, and confirming its occurrence through numerical analysis.

Contribution

It establishes the superradiant condition for Alfvén waves in Kerr magnetospheres and links it to the Blandford-Znajek process, supported by numerical reflection rate calculations.

Findings

Alfvénic superradiance occurs under specific conditions in Kerr spacetime.

Superradiance condition matches that of the Blandford-Znajek process.

Numerical simulations confirm the possibility of Alfvénic superradiance.

Abstract

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.