Study of circular geodesics and shadow of rotating charged black hole surrounded by perfect fluid dark matter immersed in plasma.

In this work, we consider a rotating charged black hole surrounded by perfect fluid dark matter \cite{1}. We consider the system to be immersed in non-magnetic, pressureless plasma. We then evaluate the null geodesics in order to study the co-rotating and counter rotating photon orbits. Later we analyse the null geodesics further, to calculate the celestial coordinates ($\alpha, \beta$). The celestial coordinates are used to determine the shadow radius ($R_s$). After that we observe and analyse the effects of black hole spacetime, perfect fluid dark matter and plasma parameters ($a$, $Q$, $\chi$, $k$) on the black hole shadow in detail. Finally, we study the effect of plasma distribution on the effective potential ($V_{eff}$) of the black hole spacetime as encountered by the photons.