The tachyonic instability of the Kerr black holes is analyzed in the Einstein-scalar theory with the quadratic scalar couplings to two topological terms which are parity-even Gauss-Bonnet and parity-odd Chern-Simons terms. For positive coupling α, we use the (2+1)-dimensional hyperboloidal foliation method to derive the threshold curve which is the boundary between stable and unstable Kerr black holes by considering a spherically symmetric scalar-mode perturbation. In case of negative coupling, a newly bound of $a\ge 0.26$ with a the rotation parameter is found for unstable Kerr black holes and its threshold curve is derived.

中文翻译：

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将标量耦合中的标量化黑洞旋转为两个拓扑项

克尔黑洞的快子不稳定性在爱因斯坦标量理论中分析，二次标量耦合到两个拓扑项，即奇偶校验高斯-博内和奇偶校验陈-西蒙斯项。对于正耦合α，我们使用 (2+1) 维双曲面叶理方法通过考虑球对称标量模式扰动来推导阈值曲线，该曲线是稳定和不稳定克尔黑洞之间的边界。在负耦合的情况下，新的界限$\mathrm{一种}\ge 0.26$用一个旋转参数被发现为不稳定克尔黑洞和其阈值曲线的。