AI 中文总结
该研究在圈量子引力混合方法下计算了有效Ashtekar-Olmedo-Singh黑洞的准正态模式谱，发现其轴向与极地扰动的等谱性破缺仍存在，且随黑洞质量平方立方根减小，同时评估了WKB近似的适用范围。
AI 中文摘要
我们在圈量子引力的混合方法框架下，研究了有效Ashtekar-Olmedo-Singh黑洞几何的轴向与极地扰动的准正态模式谱，并将结果与del-Corral和Olmedo针对 dressed度规方法此前得到的结果进行了对比。从经典方程的直接有效对应形式的模式方程出发，我们采用带帕德重求和的高阶WKB方法计算这些谱。在dressed度规方法中被声称存在的轴向与极地扰动间的等谱性破缺，在混合量子化中依然存在，偏差量级与前者有效情形相当，不过混合方案的偏差略大。两种情形下，等谱性破缺随以普朗克单位计的黑洞质量平方的立方根减小，一致地回归经典史瓦西极限。此外，我们仔细评估了WKB近似在当前有效分析中的适用性，确认了该方法仍可靠的参数区域，并指出了近似失效的特定模式情形。
英文摘要
We investigate the quasinormal mode spectra of axial and polar perturbations about the effective Ashtekar, Olmedo, and Singh black hole geometry within the hybrid approach to loop quantum gravity. We also compare our results with those previously obtained by del-Corral and Olmedo for the dressed metric approach. Starting from mode equations that are straightforward effective counterparts of the classical equations, we compute these spectra by means of a high-order WKB method with Padé resummation. The violation of isospectrality between axial and polar perturbations that was claimed to exist in the dressed metric approach persists with the hybrid quantization, with deviations of the same order of magnitude as in the former effective case, although slightly larger for the hybrid prescription. In both situations, the isospectrality breaking decreases with the cubic root of the squared black hole mass in Planck units, consistently recovering the classical Schwarzschild limit. In addition, we perform a careful assessment of the applicability of the WKB approximation to the present effective analysis, confirming the parameter regions where the method remains reliable and highlighting specific mode cases for which the approximation breaks down.
