Researchers have investigated the quasinormal mode (QNM) spectra of axial and polar perturbations in the effective Ashtekar, Olmedo, and Singh black hole geometry, within the hybrid approach to loop quantum gravity (LQG). QNMs are the "fingerprints" of black holes, analogous to the vibrations of a bell, and their study can reveal fundamental properties of spacetime in extreme gravity environments. This work compares the obtained results with those from a previous approach, the dressed metric, seeking to understand how different quantizations of gravity affect black hole properties.

The study focused on calculating these spectra using a high-order WKB method with Padé resummation, starting from mode equations that are straightforward effective counterparts of the classical equations. A key finding is the persistence of the violation of isospectrality between axial and polar perturbations, a phenomenon previously observed in the dressed metric approach. This violation, which implies that axial and polar perturbations do not decay in the same way, is maintained with the hybrid quantization approach, with deviations of similar magnitude, although slightly larger in the latter case.

The breaking of isospectrality decreases with the cubic root of the squared black hole mass, expressed in Planck units, which is consistent with the recovery of the classical Schwarzschild limit. Furthermore, the authors performed a careful assessment of the applicability of the WKB approximation, confirming the parameter regions where the method remains reliable and highlighting specific mode cases for which the approximation breaks down. These results are crucial for understanding the implications of quantum gravity in black hole phenomenology and for future gravitational wave observations.