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In this paper, we investigate the light trajectories and shadow properties in the rotating version of null naked singularity (NNS) spacetime which is derived using the Newman–Janis algorithm without complexification method. We discuss some of the geometrical properties and causal structure of Rotating Naked Singularity (RNS) spacetime. The gravitational lensing in a rotating naked singularity is analyzed, and the results are compared to those of a Kerr black hole. In the case of a Kerr black hole, the photon sphere exists for both prograde and retrograde photon orbits, whereas for RNS, the photon sphere exists only for retrograde photon orbits. As a result, the naked singularity projects an arc-shaped shadow that differs from the contour-shaped shadow cast by a Kerr black hole. [ABSTRACT FROM AUTHOR]

Astrometric observations of S-stars provide a unique opportunity to probe the nature of Sagittarius-A* (Sgr-A*). In view of this, it has become important to understand the nature and behavior of timelike bound trajectories of particles around a massive central object. It is known now that whereas the Schwarzschild black hole does not allow the negative precession for the S-stars, the naked singularity spacetimes can admit the positive as well as negative precession for the bound timelike orbits. In this context, we study the perihelion precession of a test particle in the Kerr spacetime geometry. Considering some approximations, we investigate whether the timelike bound orbits of a test particle in Kerr spacetime can have negative precession. In this paper, we only consider low eccentric timelike equatorial orbits. With these considerations, we find that in Kerr spacetimes, negative precession of timelike bound orbits is not allowed. [ABSTRACT FROM AUTHOR]