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The Newman-Janis (NJ) algorithm has been extensively used in the literatureto generate rotating black hole solutions from nonrotating seed spacetimes. Inthis work, we show, using various constants of motion, that the null geodesicequations in an arbitrary stationary and axially symmetric rotating spacetimeobtained through the NJ algorithm can be separated completely, provided thatthe algorithm is applied successfully without any inconsistency. Using theseparated null geodesic equations, we then obtain an analytic general formulafor obtaining the contour of a shadow cast by a compact object whosegravitational field is given by the arbitrary rotating spacetime underconsideration. As special cases, we apply our general analytic formula to someknown black holes and reproduce the corresponding results for black holeshadow. Finally, we consider a new example and study shadow using our analyticgeneral formula.

Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm