Long lived quasinormal modes in the effective quantum gravity

Two models for Schwarzschild-like black holes with quantum corrections, derived from the Hamiltonian constraints approach to quantum gravity while preserving general covariance, have been developed in Zhang et al. (Phys. Rev. D 111 , L081504, 2025, arXiv:2407.10168 [gr-qc]). In this work, we study the quasinormal modes of a massive scalar field and demonstrate that the spectrum includes arbitrarily long-lived modes, known as quasi-resonances. Precise calculations using the Leaver method show good agreement with WKB data and time-domain integration within the range where these methods are reliable, specifically for small field masses.