  We introduce a family of solutions of Einstein's gravity minimally coupled to
an anisotropic fluid, describing asymptotically flat black holes with "hair"
and a regular horizon. These spacetimes can describe the geometry of galaxies
harboring supermassive black holes, and are extensions of Einstein clusters to
include horizons. They are useful to constrain the environment surrounding
astrophysical black holes, using electromagnetic or gravitational-wave
observations. We compute the main properties of the geometry, including the
corrections to the ringdown stage induced by the external matter and fluxes by
orbiting particles. The leading order effect to these corrections is a
gravitational-redshift, but gravitational-wave propagation is affected by the
galactic potential in a nontrivial way, and may be characterized with future
observatories.
