Comment on "Superradiant stability of the Kerr black holes'' by Huang

It has been claimed in \cite{1} that this research investigates the superradiant stability of a system comprising a Kerr black hole and a massive scalar perturbation. Previous studies have demonstrated superradiant stability under the condition $\mu \geq \sqrt{2} m \Omega_H$, where $\mu$ represents the scalar's proper mass, $m$ denotes the azimuthal number of the scalar mode, and $\Omega_H$ is the angular velocity of the Kerr black hole's horizon. Their work serves as a complement to these findings. They analytically establish that in the complementary parameter space, $\mu < \sqrt{2} m \Omega_H$, the system maintains superradiant stability if the scalar perturbation and Kerr black hole parameters meet two straightforward criteria: $\omega < \frac{\mu}{\sqrt{2}}$ and $\frac{r_{-}}{r_{+}} < 0.802$.The condition derived therein involves four variables (\(z_1\), \(z_2\), \(z_3\), and \(z_4\)) which are all negative. Given the focus of the cited article on analyzing the stability condition of \(B_1\), imposing constraints on the sign (positive or negative) of \(z_1\) and \(z_2\) is not pertinent. Consequently, the stability criterion presented in this article is broader and less precise.