Black holes surrounded by generic dark matter profiles: Appearance and gravitational-wave emission

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 extends previous studies showing that modifications of orbital frequencies and axial fluxes can be described in terms of gravitational redshift, regardless of the halo model.