  Naked singularities are hypothetical astrophysical objects, characterized by
a gravitational singularity without an event horizon. Penrose has proposed a
conjecture, according to which there exists a cosmic censor who forbids the
occurrence of naked singularities. Distinguishing between astrophysical black
holes and naked singularities is a major challenge for present day
observational astronomy. A possibility of differentiating naked singularities
from black holes is through the comparative study of thin accretion disks
properties around rotating naked singularities and Kerr-type black holes,
respectively. In the present paper, we consider accretion disks around rotating
naked singularities, obtained as solutions of the field equations in the
Einstein-massless scalar field theory. A first major difference between
rotating naked singularities and Kerr black holes is in the frame dragging
effect, the angular velocity of a rotating naked singularity being inversely
proportional to its spin parameter. Due to the differences in the exterior
geometry, the thermodynamic and electromagnetic properties of the disks are
different for these two classes of compact objects, consequently giving clear
observational signatures that could discriminate between black holes and naked
singularities. For specific values of the spin parameter and of the scalar
charge, the energy flux from the disk around a rotating naked singularity can
exceed by several orders of magnitude the flux from the disk of a Kerr black
hole. The conversion efficiency of the accreting mass into radiation by
rotating naked singularities is always higher than the conversion efficiency
for black holes. Thus, these observational signatures may provide the necessary
tools from clearly distinguishing rotating naked singularities from Kerr-type
black holes.
