  Repulsive gravity is a well known characteristic of naked singularities. In
this work, we explore light surfaces and find new effects of repulsive gravity.
We compare Kerr naked singularities with the corresponding black hole
counterparts and find certain structures that are identified as horizon
remnants. We argue that these features might be significant for the
comprehension of processes that lead to the formation or eventually destruction
of black hole Killing horizons. These features can be detected by observing
photon orbits, particularly close to the rotation axis, which can be used to
distinguish naked singularities from black hole.
