  We compute quasinormal mode frequencies for static limits of physical black
holes - semi-classical 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 non-trivial 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 semi-classical setting, and demonstrate
the potential for mimicking signatures of axially-symmetric geometries from a
spherically-symmetric source.
