Semiclassical imprints on quasinormal mode spectra

We compute quasinormal mode frequencies for static limits of physical black holes - semiclassical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity. These assumptions lead to a highly constrained yet nontrivial form of the metric and components of the energy-momentum tensor near the horizon, which contain as a special case many known models of black holes. Using a two-point M-fraction approximation to construct an interpolating metric which captures the essential near-horizon and asymptotic properties of black holes, we explore a large part of the parameter space that characterizes the near-horizon geometry. We cast the perturbation problem as a discretized homogeneous eigensystem and compute the low-lying quasinormal mode frequencies for perturbations of a massless scalar field. Working in spherical symmetry, we provide rough constraints on leading and subleading deviations from the Schwarzschild solution which arise in a semiclassical setting.