  Black holes are a paradigm in nowadays physics, and are expected to be hosted
at the center of galaxies. Supermassive galactic black holes are not isolated,
and their surroundings play crucial roles in many observational features. The
absorption and scattering of fields by isolated black holes have been vastly
studied, allowing the understanding of many phenomenological features. However,
as far as we are aware, a study of the influence of the presence of matter
surrounding black holes in its planar wave scattering and absorption spectrum
is still lacking in the literature. This may be important in the analysis of,
for instance, the accretion of dark matter by black holes. We consider planar
massless scalar waves incident upon a Schwarzschild black hole surrounded by a
thin spherical shell. We use the partial wave method to determine the
absorption cross section, and present a selection of numerical results. In the
low-frequency regime, we show that the absorption cross section is equal to the
horizon area. At the high-frequency regime, we show that the absorption cross
section approaches the geodesic capture cross section.
