Kerr black hole surrounded by dark matter: Horizon, photonosphere and shadow - Pantig, Reggie C. (Animo Repository, 2019)
We study the effect of a simple spherical model of dark matter with mass D and thickness Δr to a Kerr black hole of mass M. It is shown that the horizon and ergosphere radii are affected. We utilize the Hamilton-Jacobi equation in deriving the equations of motion to study the photonsphere and generate a black hole shadow image. For increasing D and fixed Δr, the radial distance of the photon's last unstable prograde orbit tends to increase as the Kerr black hole approaches extremality. The condition also makes the photon's last unstable retrograde orbit to decrease in distance from the black hole. These results to the black hole's shadow radius to increase. Dramatic distortion to black hole shadow can occur if the dark matter density is abnormally high. A very low dark matter density results to an almost negligible effect to the black hole shadow. The expression for the condition such that the noticeable effect of dark matter starts to occur is rather cumbersome. A study of this kind can pave a way for sophisticated future observations to indirectly detect dark matter, if there is any.