Peculiar properties in quasi-normal spectra from loop quantum gravity effect

Abstract: We investigate the quasi-normal mode (QNM) spectra for scalar and electromagnetic fields over a covairant loop quantum gravity black hole (LQG-BH). For the fundamental modes, the LQG effect reduces the oscillations in the scalar field, however it induces stronger oscillations in the electromagnetic field, comparing to the classical case. Under the scalar field perturbation, the system enjoys faster decaying modes with more oscillations than the electromagnetic field. Some peculiar phenomena emerge in the QNM spectra with higher overtones. A notable feature is the substantial divergence observed in the first several overtones from their Schwarzschild counterparts, with this discrepancy magnifying as the overtone number increases. Another remarkable phenomenon in higher overtones is that the QNFs of the scalar field with $l=0$ exhibit an oscillatory behavior as the quantum parameter $r_0$ increases significantly. These oscillations intensify with the rising overtone number. We hypothesize that this oscillatory pattern may be associated with the extremal effect.