While ‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher resembles that in four‐dimensional spacetime with the corresponding asymptotic.

中文翻译：

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(2+1)$(2+1)$‐维渐近平坦、dS 和 AdS 黑洞的拟正态谱

虽然爱因斯坦理论中的 维黑洞仅允许反德西特 (AdS) 渐进，但当打开更高曲率校正时，渐近平坦、德西特和 AdS 情况都包括在内。在这里，提出了对具有所有三个渐近的黑洞周围标量场扰动的稳定性和拟正规谱的详细研究。频率的计算是借助带有 Pade 近似的六阶 Wentzel-Kramers-Brillouin (WKB) 方法、Bernstein 多项式方法和时域积分来完成。所有三种方法获得的结果在其共同的适用范围内非常一致。当多极矩等于零时，纯虚数（即非振荡）模式在所有类型渐近行为的频谱中占主导地位，而更高的频谱类似于具有相应渐近行为的四维时空中的频谱。