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 at all they exist in nature, can be distinguished from black
holes. We study the gravitational lensing in the strong field regime in the JMN
spacetime, a spherically symmetric geometry that contains a naked singularity
and which matches smoothly with Schwarzschild metric beyond a finite radius.
This metric is a toy model which was shown recently to be the end state of
gravitational collapse. In the presence of the photon sphere gravitational
lensing signature of this spacetime is identical to that of 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. The results obtained here are in contrast with
the earlier investigation on JNW naked singularities radial caustic was always
present in the absence of photon sphere, while it is absent in JMN geometry. 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 must be developed in future for this purpose.
