The present paper is a follow-up of our previous paper that derives a slightly simplified model equation for the Klein-Gordon equation, describing the propagation of a scalar field of mass μ in the background of a rotating black hole and, among others, supports the instability of the field down to a/M ≈ 0.97. The latter result was derived numerically. This paper gives corresponding rigorous results, supporting instability of the field down to a/M ≈ 0.979796.

中文翻译：

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克尔时空 Klein-Gordon 方程模型的稳定性研究 II

本论文是我们之前论文的后续论文，该论文推导出了 Klein-Gordon 方程的稍微简化的模型方程，描述了质量为μ的标量场在旋转黑洞的背景下的传播，其中支持场的不稳定性下降到a/M ≈ 0.97。后一个结果是从数值上推导出来的。本文给出了相应的严格结果，支持低至a/M ≈ 0.979796的场不稳定性。