Extremal rotating black holes, scalar perturbation and superradiant stability

Understand

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.