Rotating dirty black hole and its shadow.

In this paper, we examine the effect of dark matter to a Kerr black hole of mass $m$. The metric is derived using the Newman-Janis algorithm, where the seed metric originates from the metric of a Schwarzschild black hole surrounded by a spherical shell of dark matter with mass $M$ and thickness $\Delta r_{s}$. We analyzed both the time-like and null geodesics and found out that if the dark matter density is considerably low, time-like geodesics shows more deviations from the Kerr case compared to null geodesics. Furthermore, energy extraction via the Penrose process remains unchanged. A high concentration of dark matter near the rotating black hole is needed to have considerable deviations on the horizons and photonsphere radius. With the dark matter configuration used in this study, we found that deriving an analytic estimate to determine the condition for dark matter to have a notable change in the shadow radius is inconvenient.