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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 2 m H, where represents the scalar's proper mass, m denotes the azimuthal number of the scalar mode, and 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, < 2 m H, the system maintains superradiant stability if the scalar perturbation and Kerr black hole parameters meet two straightforward criteria: < 2 and r-r+ < 0. 802. The condition derived therein involves four variables (\ (z₁\), \ (z₂\), \ (z₃\), and \ (z₄\) ) which are all negative. Given the focus of the cited article on analyzing the stability condition of \ (B₁\), imposing constraints on the sign (positive or negative) of \ (z₁\) and \ (z₂\) is not pertinent. Consequently, the stability criterion presented in this article is broader and less precise.
Wen-Xiang Chen (Fri,) studied this question.
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