Shadow and Deflection Angle of Rotating Black Holes in Perfect Fluid Dark Matter with a Cosmological Constant

Abstract

The presence of dark matter around a black hole remarkably affects its spacetime. We consider the effects of dark matter on the shadow of a new solution to the Einstein equations that describes a rotating black hole in the background of perfect dark matter fluid (PFDM), along with its extension to nonzero cosmological constant $Λ$. Working in Boyer-Lindquist coordinates, we consider the effects of the PFDM parameter $α$ on the shadow cast by a black hole with respect to an observer at position $(r_o,θ_o)$. By applying the Gauss-Bonnet theorem to the optical geometry we find that notable distortions from a Kerr black hole can occur. We describe their dependence on $α$ and $Λ$.

15 pages, 4 figures. Accepted for publication in Physical Review D