Rotating dirty black hole and its shadow

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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 Schwarzschild black hole surrounded by a spherical shell of dark matter with mass $M$ and thickness $\Delta r_{s}$.
• The seed metric is also described in terms of a piecewise mass function with three different conditions.
• Specializing in the non-trivial case where the observer resides inside the dark matter shell, we analyzed how the effective mass of the black hole environment affects the basic black hole properties.