Analysis on superradiant stability of BTZ Black Hole

This paper adds a new variable y($μ^{\prime}=y(ω+m N^ϕ)$) 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 $\sqrt{2(m^2)}/{ r^2_+}< ω< m\varOmega_H$,so the BTZ black hole was superradiantly stable at that time.

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