Black Hole in the Quantum Oppenheimer–Snyder Model: Long Lived Modes and the Overtones' Behavior

Abstract A quantum‐corrected black hole metric has been derived in [Lewandowski et al., Phys. Rev. Lett. 130 (2023) 10, 101501] within the context of the quantum Oppenheimer–Snyder model inspired by loop quantum cosmology. Using the Frobenius method, we have obtained precise values for the fundamental quasinormal modes and the first few overtones for scalar and electromagnetic perturbations. Our results reveal that, unlike the fundamental mode, the overtones exhibit high sensitivity to quantum corrections, leading to qualitatively new spectral behavior. Notably, our findings suggest that modes with real oscillation frequencies approaching zero appear in the spectrum. The existence of arbitrarily long‐lived modes, known as quasi‐resonances is also demonstrated.