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

It has been claimed in {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 μ ≥ √2 m ΩH, where μ represents the scalar's proper mass, m denotes the azimuthal number of the scalar mode, and ΩH 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, μ < √2 m ΩH, the system maintains superradiant stability if the scalar perturbation and Kerr black hole parameters meet two straightforward criteria: ω < μ√2 and 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.