Rotating reduced Kiselev black holes: Shadows, Energy emission and Deflection of light

In this paper, we generate a rotating solution of the reduced Kiselev black hole through the Newman-Janis formalism. Based on such solution, we remark different shadow behaviors by varying the involved parameters $r_k, a, \alpha$. Concretely, we observe that the allowed values of the spin parameter $a$ are much less than the usual rotating black holes. By deeply analysing the shadow shapes, we show that comparable shadow shapes emerge for the same ratio $a/r_k$. On the other hand, we recognize that the parameters $a$ and $\alpha$ governs the shadow geometry while the parameter $r_k$ rules the size of such a quantity. Besides, we notice that an elliptic shadow geometry appears for certain range of relevant parameters. By making contact with the observational side, we provide a constraint on the rotating reduced Kiselev (RRK) black hole parameters. In particular, we find a good compatibility between the theoretical and experimental results. Regarding Hawking radiation, we note that the Kiselev radius $r_ k$ shows a similar behavior to the quintessence filed intensity $\mathbf{c}$. Concerning the light motion in the vicinity of a RRK black hole, we investigate deeply the deflection by varying the relevant parameters. In particular, we remark that such a quantity decreases by increasing the parameters $a$ and $\alpha$ while the opposite effect is observed when increasing $r_k$.