As the fingerprints of black holes, quasinormal modes are closely associated with many properties of black holes. Especially, the ringdown phase of gravitational waveforms from the merger of compact binary components can be described by quasinormal modes. Serving as a model-independent approach, the framework of parametrized quasinormal frequencies offers a universal method for investigating quasinormal modes of diverse black holes. In this work, we first obtain the Schrödinger-like master equation of the axial gravitational perturbation of a holonomy-corrected black hole. We calculate the corresponding quasinormal frequencies using the Wentzel-Kramers-Brillouin approximation and asymptotic iteration methods. We investigate the numerical evolution of an initial wave packet on the background spacetime. Then, we deduce the parametrized expression of the quasinormal frequencies and find that $r_0\le {10}^{-2}$ is a necessary condition for the parametrized approximation to be valid, where $r_0$ is the quantum parameter. We also study the impact of the parameter $r_0$ on the greybody factor and Hawking radiation. With more ringdown signals of gravitational waves detected in the future, our research will contribute to the study of the quantum properties of black holes.

中文翻译：

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完整校正黑洞轴向引力扰动的参数化准正态频率和霍金辐射


准正规模作为黑洞的指纹，与黑洞的许多性质密切相关。特别是，致密二元分量合并产生的引力波形的衰荡阶段可以用拟正规模来描述。作为一种独立于模型的方法，参数化准正规频率框架为研究不同黑洞的准正规模式提供了一种通用方法。在这项工作中，我们首先获得了完整校正黑洞的轴向引力摄动的类薛定谔主方程。我们使用 Wentzel-Kramers-Brillouin 近似和渐近迭代方法计算相应的拟正态频率。我们研究背景时空中初始波包的数值演化。然后，我们推导拟正规频率的参数化表达式，发现 $r_0\le {10}^{-2}$ 是参数化近似有效的必要条件，其中 $r_0$ 是量子参数。我们还研究了参数的影响 $r_0$ 关于灰体因子和霍金辐射。随着未来检测到更多引力波振铃信号，我们的研究将为黑洞量子特性的研究做出贡献。