In this paper, we derive general conditions for a shadow to occur, without a photon sphere in a spacetime, caused by central nulllike or timelike naked singularities. Using these conditions, we propose classes of spacetimes which have nulllike and timelike naked singularities at the center, and that fulfill these ‘shadow without photon sphere’ conditions. Considering additional asymptotically flat conditions, we show that, for a fixed Schwarzschild mass, the timelike naked singularities can cast a shadow of a size that is equal to, greater or smaller, than the size of a black hole shadow. On the other hand, the size of shadow of a nulllike naked singularity is always less than that of a black hole. Such novel features of shadows of nulllike and timelike naked singularities in the absence of photon spheres may help us to distinguish between black holes and naked singularities observationally.

It is now known that the shadow is not only the property of a black hole, it can also be cast by other compact objects like naked singularities. However, there exist some novel features of the shadow of the naked singularities which are elaborately discussed in some recent articles. In the earlier literature, it is also shown that a naked singularity may admit negative precession of bound timelike orbits which cannot be seen in Schwarzschild and Kerr black hole spacetimes. This distinguishable behavior of timelike bound orbit in the presence of the naked singularity along with the novel features of the shadow may be useful to distinguish between a black hole and a naked singularity observationally. However, in this paper, it is shown that deformed Kerr spacetime can allow negative precession of bound timelike orbits, when the central singularity of that spacetime is naked. We also show that negative precession and shadow both can exist simultaneously in deformed Kerr naked singularity spacetime. Therefore, any observational evidence of negative precession of bound orbits, along with the central shadow may indicate the presence of a deformed Kerr naked singularity.

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.

In this paper, we construct the rotating Janis–Newman–Winicour (JNW) naked singularity spacetime using Newman–Janis Algorithm (NJA). We analyse NJA with and without complexification methods and find that the energy conditions do satisfied when we skip the complexification step. We study the shadows cast by rotating JNW naked singularity and compare them with the shadows cast by the Kerr black hole. We find that the shadow of the rotating naked singularity can be distinguished from the shadow of the Kerr black hole. While we analyse the precession of timelike bound orbits in rotating JNW spacetime, we find that it can have a negative (or opposite) precession, which is not present in the Kerr black hole case. These novel signatures of the shadow and orbital precession in rotating JNW naked singularity spacetime could be important in the context of the recent observation of the shadow of the M87 galactic center and the stellar dynamics of ‘S-stars’ around Milkyway galactic center.

It is now known that, apart from black holes, some naked singularities can also cast shadows which provide their possible observable signatures. We examine the relevant question here as to how to distinguish then these entities from each other, in terms of further physical signatures. In earlier literature, it has been pointed out that the Schwarzschild black holes always admit timelike bound orbits having positive perihelion precession. It has been also shown, while some naked singularities [e.g., Joshi-Malafarina-Narayan spacetime (JMN)] with a photon sphere can cast a shadow, it could also admit positive perihelion precession for such orbits, thereby mimicking a Schwarzschild black hole. This indicates that nonspinning compact objects with photon spheres may always admit positive perihelion precession of timelike bound orbits around them. In this paper, we construct a static, nonrotating spacetime configuration which has a central naked singularity but no photon sphere, and it can give both shadow and a negative perihelion precession. In the present case, the shadow is cast by a spherically symmetric thin shell of matter, not by a photon sphere. Our results imply that, whereas the presence of a shadow and a positive perihelion precession implies either a Schwarzschild black hole or a naked singularity, the presence of a shadow and a negative perihelion precession simultaneously may imply a naked singularity only. We discuss our results in the context of stellar motions (motion of the “S” stars) around the Sgr-A* galactic center.

We investigate here the local versus global visibility of a spacetime singularity formed due to the gravitational collapse of a spherically symmetric dust cloud having a nonzero velocity function. The conditions are investigated that ensure the global visibility of the singularity, in the sense that the outgoing null geodesics leave the boundary of the matter cloud in the future, whereas, in the past, these terminate at the singularity. Explicit examples of this effect are constructed. We require that this must be a strong curvature singularity in the sense of Tipler, to ensure the physical significance of the scenario considered. This may act as a counterexample to the weak cosmic censorship hypothesis.