  We develop a numerical approach to find asymptotically flat black hole
solutions coupled to anisotropic fluids, described by generic density profiles.
Our model allows for a variety of applications in realistic astrophysical
scenarios, and is potentially able to describe the geometry of galaxies hosting
supermassive black holes, dark matter environments and accretion phenomena. We
apply our framework to a black hole surrounded by different families of dark
matter profiles, namely the Hernquist, the Navarro-Frenk White and the Einasto
models. We study the geodesic motion of light and of massive particles in such
spacetimes. Moreover we compute gravitational axial perturbations induced by a
small secondary on the numerical background, and determine the changes in the
emitted gravitational wave fluxes compared to the vacuum case. Our analysis
confirms and extend previous studies showing that modifications of orbital
frequencies and axial fluxes can be described in terms of
gravitational-redshift, regardless of the halo model.
