Quasi-Normal Modes of Covariant Loop Quantum Black Holes

Abstract

We investigate the quasinormal modes (QNMs) and time-domain response of a massless, minimally coupled test scalar field on static, spherically symmetric covariant loop quantum black hole (cLQBH) backgrounds. Focusing on a phenomenological, Gaussian-localized holonomy profile, we obtain a localized deformation of the scalar effective potential containing both positive and negative parts. This provides a geometric realization of the bump effect, with the potential deformation and tortoise-coordinate mapping determined consistently by the same background. We characterize the deformation by its location, amplitude, and width, and study its effects using frequency-domain shooting and time-domain evolution, supplemented by matrix-pencil mode extraction and waveform reconstruction. The QNM spectrum exhibits spiral trajectories as the bump location varies, enhanced sensitivity of the overtones, and mode overtaking, whereby the branch continued from the first Schwarzschild overtone becomes longer-lived than the continued fundamental branch. Despite substantial spectral changes, the early response can remain close to its Schwarzschild counterpart, with more pronounced differences emerging later. To quantify this behavior, we introduce a local waveform-deviation time and compare it with a relative-amplitude faintness time, thereby defining an operational observation window. The deviation time depends nonmonotonically on the bump location, and suitable parameter choices allow appreciable departures to emerge before the adopted faintness threshold is reached. These results connect localized holonomy corrections with spectral sensitivity and waveform evolution, providing a basis for future gravitational-perturbation studies and assessments of gravitational-wave detectability.