Parameterized quasinormal frequencies and Hawking radiation for axial gravitational perturbations of a holonomy-corrected black hole

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 parameterized quasinormal frequencies offers a universal method for investigating quasinormal modes of diverse black holes. In this work, we first obtain the Schr\"{o}dinger-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 parameterized expression of the quasinormal frequencies and find that $r_0 \leq 10^{-2}$ is a necessary condition for the parameterized approximation to be valid. We also study the impact of the quantum 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.