Probing the effective quantum gravity via quasinormal modes and shadows of black holes

Two quantum-corrected black hole models have recently been proposed within the Hamiltonian constraints approach to quantum gravity, maintaining general covariance [Phys. Rev. D 111, L081504 (2025).]. We have studied in detail the quasinormal spectra of test fields and axial gravitational perturbations of these black holes using various methods. The two models differ in their choice of quantum parameter $\ensuremath{\xi}$, and we can distinguish them by their quasinormal spectra. In the first model, increasing the quantum parameter results in higher real oscillation frequencies and damping rates of the fundamental mode. In contrast, the second model shows a decrease in the oscillation frequency of the…