Can strong gravitational lensing distinguish naked singularities from black holes?

In this paper we study gravitational lensing in the strong field limit from the perspective of cosmic censorship, to investigate whether or not naked singularities, if they exist in nature at all, can be distinguished from black holes. The spacetime we explore from this perspective is the Joshi-Malafarina-Narayan (JMN) metric which represents a spherically symmetric solution to the Einstein field equations with anisotropic pressure and contains a naked singularity at the center. JMN geometry is matched with the Schwarzschild metric to the exterior at a finite radius. This metric was recently shown to be a possible end state of gravitational collapse of a fluid with zero radial pressure. In the presence of the photon sphere, gravitational lensing signature of this spacetime is identical to that of the Schwarzschild black hole with infinitely many relativistic images and Einstein rings, all of them located beyond a certain critical angle from optic axis and the inner relativistic images all clumped together. However, in the absence of the photon sphere, which is the case for a wide range of parameter values in this spacetime, we show that we get finitely many relativistic images and Einstein rings spaced reasonably apart from one another, some of which can be formed inside the critical angle for the corresponding Schwarzschild black hole. This study suggests that the observation of relativistic images and rings might, in principle, allow us to unravel the existence of the naked singularity in the absence of the photon sphere. Also, the results obtained here are in contrast with the earlier investigation on Janis-Newman-Winicour (JNW) naked singularities where it was shown that the radial caustic is always present in the absence the photon sphere, which is not the case with JMN geometry where radial caustic is absent. We also point out the practical difficulties that might be encountered in the observation of the relativistic images and suggest that new dedicated experiments and techniques have to be developed in future for this purpose.