Analysis on superradiant stability of BTZ Black Hole

TL;DR

This paper investigates the superradiant stability of BTZ black holes by introducing a new variable and analyzing the effective potential, concluding stability conditions based on the potential's properties.

Contribution

It extends previous analyses by incorporating a new variable and utilizing curve integrals to determine stability conditions for BTZ black holes.

Findings

No potential well outside the horizon when y exceeds a certain limit.

Superradiant stability occurs within specific frequency bounds.

Effective potential analysis confirms stability under these conditions.

Abstract

This paper adds a new variable y($\mu^{\prime}=y(\omega+m N^{\phi})$) to extend the results of the classic paper. We exploit the properties of curve integrals. When y is greater than a certain limit, the effective potential of the equation has no pole, then there is no potential well outside the event horizon, when $\sqrt{2(m^2)}/{ r^2_+}< \omega < m\varOmega_H$,so the BTZ black hole was superradiantly stable at that time.