Lensing by black holes within astrophysical environments

Astrophysical black holes are likely to be surrounded by various forms of matter in the form of disks or halos. While a number of studies have examined the impact of an environment on the lensing of light or gravitational waves from cosmological sources, these have, thus far, been carried out in either a Newtonian or post-Newtonian framework where the environment is superimposed on the black-hole spacetime. By using an exact solution in general relativity describing a black hole embedded within a realistic halo of Hernquist matter distribution, we study deflection angles and image amplification in a fully relativistic setup. It is shown that large ``bumps,'' that also arise at the Newtonian and post-Newtonian levels, track the transition scale set by the halo parameters that control the strong-lensing upturn and can significantly adjust the inferences made for either the source or lens in various contexts. As an application, we consider ``echoes'' of gravitational waves, sourced by astrophysical lenses rather than being intrinsic to the compact object that produces the signal.