Absorption by dirty black holes: Null geodesics and scalar waves

Black holes are a paradigm in physics nowadays and are expected to be hosted at the centers 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 their 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.