Quantum dust cores of black holes and their quasi-normal modes

The quantum description of a gravitationally collapsed ball of dust proposed in Ref.~\cite{Casadio:2023ymt} is characterised by a linear effective Misner-Sharp-Hernandez mass function describing a matter core hidden by the event horizon. After reviewing the original model and some of its refinements, we investigate the quasi-normal mode spectrum of the resulting spacetime and compare it with the Schwarzschild case. Computations are performed within the WKB approximation, based on the Pad\'e approximants up to thirteenth order. Our analysis shows that deviations from the Schwarzschild spectrum are sensitive to the quantum nature of the core surface.