Greybody Factor for a Rotating Bardeen Black Hole by Perfect Fluid Dark Matter

In this paper, the greybody factor is studied analytically for a rotating regular Bardeen black hole surrounded by perfect fluid dark matter. Firstly, we examine the behavior of effective potential by using the radial equation of motion developed from the Klein-Gordon equation. We then consider tortoise coordinate to convert the radial equation into Schr\"odinger form equation. We solve the radial equation of motion and obtain two different asymptotic solutions in terms of hypergeometric function measured at distinct regimes so called near and far-field horizons. These solutions are smoothly matched over the whole radial coordinate in an intermediate regime to check their viability. Finally, we measure the absorption probability for massless scalar field and examine the effect of perfect fluid dark matter. It is concluded that both the effective potential and greybody factor increase with perfect fluid dark matter.