Superradiant instability in slowly rotating Kerr-Newman black holes

TL;DR

This paper investigates the superradiant instability of slowly rotating Kerr-Newman black holes under charged scalar perturbations, concluding that such instability is unlikely without a reflecting cavity, and identifies conditions for quasibound states.

Contribution

It provides a detailed analysis showing superradiant instability is suppressed in slowly rotating Kerr-Newman black holes and derives conditions for quasibound states.

Findings

Superradiant instability is not allowed in sKN black holes without a cavity.

Negative absorption cross section observed in low frequency scattering.

Conditions for quasibound states are established.

Abstract

We study the superradiant instability of slowly rotating Kerr-Newman (sKN) black holes under a charged massive scalar perturbation. These black holes resemble closer the Reissner-Nordstr\"{o}m black holes than the Kerr-Newman black holes. We compute the negative absorption cross section of a massive scalar for superradiant scattering in the low frequency limit. From the scalar potential analysis, we find that the superradiant instability is not allowed in the sKN black holes because the condition for a trapping well is not compatible with the superradiance condition. However, the rate of energy extraction might grow exponentially if the sKN black hole is placed inside a reflecting cavity. Finally, we obtain the condition for the trapping well to possess quasibound states in the sKN black holes by analyzing asymptotic scalar potential and wave functions.