  It is commonly thought that the final product of gravitational collapse is a
black hole. Nevertheless, theoretical studies have not yet provided a final
answer to the question whether black holes are the only possible outcome or
whether naked singularities are also allowed. Observational tests may thus
represent a complementary approach. In the present paper, we consider the
Janis-Newman-Winicour metric, which describes a rotating source with a
surface-like naked singularity. We calculate iron line shapes in the reflection
spectrum of a putative disk around a Janis-Newman-Winicour singularity and we
compare our results with the iron line shapes expected in the spectrum of a
Kerr black hole. While it is difficult to distinguish the two spacetimes from
the iron line shape in general, it seems that Janis-Newman-Winicour
singularities cannot mimic fast-rotating Kerr black holes observed at a low or
moderate inclination angle. Our analysis thus suggests that available
observations of specific sources can already constrain the possible existence
of Janis-Newman-Winicour singularities in the Universe.
