We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked singularity spacetime restricted to radii r ≤ R b , matched to Schwarzschild spacetime outside the boundary radius R b . While a black hole always has a photon sphere and always casts a shadow, we find that the naked singularity models have photon spheres only if a certain parameter M 0 that characterizes these modelswhere M is the total mass of the object. Such models do produce shadows. However, models with M 0 < 2/3 (or R b > 3M) have no photon sphere and do not produce a shadow. Instead, they produce an interesting "full-moon" image. These results imply that the presence of a shadow does not by itself prove that a compact object is necessarily a black hole. The object could be a naked singularity with M 0 ≥ 2/3, and we will need other observational clues to distinguish the two possibilities. On the other hand, the presence of a full-moon image would certainly rule out a black hole and might suggest a naked singularity with M 0 < 2/3. It would be worthwhile to generalize the present study, which is restricted to spherically symmetric models, to rotating black holes and naked singularities.

We study shadows cast by a certain class of rotating wormholes and point out the crucial role of a rotating wormhole throat in the formation of a shadow. Overlooking this crucial role of a wormhole throat has resulted incomplete results in the previous studies on shadows of the same class of rotating wormholes. We explore the dependence of the shadows on the spin of the wormholes.We compare our results with that of the Kerr black hole. With increasing values of the spin, the shapes of the wormhole shadows start deviating considerably from that of the black hole. Such considerable deviation, if detected in future observations, may possibly indicate the presence of a wormhole. In other words, the results obtained here indicate that, through the observations of their shadows, the wormholes which are considered in this work and have reasonable spin, can be distinguished from a black hole. * rajibul.shaikh@tifr.res.in

The Newman-Janis (NJ) algorithm has been extensively used in the literature to generate rotating black hole solutions from nonrotating seed spacetimes. In this work, we show, using various constants of motion, that the null geodesic equations in an arbitrary stationary and axially symmetric rotating spacetime obtained through the NJ algorithm can be separated completely, provided that the algorithm is applied successfully without any inconsistency.Using the separated null geodesic equations, we then obtain an analytic general formula for obtaining the contour of a shadow cast by a compact object whose gravitational field is given by the arbitrary rotating spacetime under consideration. As special cases, we apply our general analytic formula to some known black holes and reproduce the corresponding results for black hole shadow. Finally, we consider a new example and study shadow using our analytic general formula. * rshaikh@iitk.ac.in

We study here images of thin accretion disks around black holes and two classes of naked singularity spacetimes and compare these scenarios. The naked singularity models which have photon spheres have single accretion disk with its inner edge lying outside the photon sphere. The images and shadows created by these models mimic those of black holes. It follows, therefore, that further and more detailed analysis of the images and shadows structure in such case is needed to confirm or otherwise the existence of an event horizon for the compact objects such as the galactic centers. However, naked singularity models which do not have any photon spheres can have either double disks or a single disk extending up to the singularity. The images obtained from such models significantly differ from those of black holes. Moreover, the images of the two classes of naked singularities in this latter case, differ also from one another, thereby allowing them to be distinguish from one another through the observation of the images. * rshaikh@iitk.ac.in † psjprovost@charusat.ac.in

We study strong gravitational lensing by a class of static wormhole geometries. Analytical approaches to the same are developed, and the results differ substantially from strong lensing by black holes, first reported by Bozza. We consider two distinct situations, one in which the observer and the source are on the same side of the wormhole throat, and the other in which they are on opposite sides. Distinctive features in our study arise from the fact that photon and antiphoton spheres might be present on both sides of the wormhole throat, and that the throat might itself act as a photon sphere. We show that strong gravitational lensing thus opens up a rich variety of possibilities of relativistic image formation, some of which are novel, and are qualitatively distinct from black hole lensing. These can serve as clear indicators of exotic wormhole geometries.