  Direct imaging of supermassive black holes (SMBHs) at event horizon scale
resolutions, as recently done by the Event Horizon Telescope, allows for
testing alternative models to SMBHs such as Kerr naked singularities (KNSs). We
demonstrate that the KNS shadow can be closed, open, or vanishing, depending on
the spins and observational inclination angles. We study the critical
parameters where the KNS shadow opens a gap, a distinctive phenomenon that does
not happen with the black hole shadow. We show that the KNS shadow can only be
closed for dimensionless spin $a \lesssim 1.18$ and vanishing for $a \gtrsim
1.18$ for certain ranges of inclination angles. We further analyze the
effective angular momentum of photon orbits to demonstrate the fundamental
connections between light geodesics and the KNS shadow geometry. We also
perform numerical general relativistic ray tracing calculations, which
reproduce the analytical topological change in the KNS shadow and illustrate
other observational features within the shadow due to the lack of an event
horizon. By comparing with black hole shadow observations, the topological
change in the shadow of KNSs can be used to test the cosmic censorship
hypothesis and KNSs as alternative models to SMBHs.
