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

TL;DR

This paper investigates how perfect fluid dark matter and a cosmological constant influence the shadow and deflection angles of rotating black holes, revealing notable distortions from Kerr black holes.

Contribution

It introduces a new solution for rotating black holes in perfect fluid dark matter with a cosmological constant and analyzes their shadow distortions.

Findings

Dark matter parameter $\alpha$ significantly affects black hole shadows.

Cosmological constant $\Lambda$ influences shadow shape and size.

Distortions from Kerr black holes depend on $\alpha$ and $\Lambda$.

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 $\Lambda$. Working in Boyer-Lindquist coordinates, we consider the effects of the PFDM parameter $\alpha$ on the shadow cast by a black hole with respect to an observer at position $(r_o,\theta_o)$. 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 $\alpha$ and $\Lambda$.