Analysis on superradiant stability of BTZ Black Hole

This paper adds a new variable y(${\mu }^{\mathrm{\prime }}=y(\omega +m{N}^{\varphi })$) 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 $\sqrt{2(m^2)}\mathrm{/}{r}_{+}^2<\omega <m{\Omega }_H$,so the BTZ black hole was superradiantly stable at that time.