  We numerically solve the mass-less test scalar field equation on the
space-time background of boson stars and black holes. In order to do so, we use
a numerical domain that contains future null infinity. We achieve this
construction using a scri-fixing conformal compactification technique based on
hyperboloidal constant mean curvature foliations of the space-time and solve
the conformally invariant wave equation. We present two results: the scalar
field shows oscillations of the quasi- normal-mode type found for black holes
only for boson star configurations that are compact, and no signs of tail decay
is found in the parameter space we explored. Even though our results do not
correspond to the master equation of perturbations of boson star solutions,
they indicate that the parameter space of boson stars as black hole mimickers
is restricted to compact configurations.
