What happens when you dump antimatter onto a naked singularity? Inspired by this question, what would happen if you dumped antimatter onto a naked singularity? The answers for the previous question suggest that once the antimatter crossed the event horizon, no annihilation reaction would occur and its mass-energy would be added to that of the black hole.
However, it's possible for rotating black holes to lack an event horizon, creating a naked singularity. What would happen if such a naked singularity were to be exposed to a considerable amount of anti-matter? Would the anti-matter be assimilated into the singlularity, pass by it unaffected, or would there be some sort of reaction?
 A: The reason why naked curvature singularities are a no good very bad just the worst object for physicists is the fact that there is no theory of their dynamical behavior, and no real predictions can be given for their appearances or interactions with their environments. If you do take a curvature singularity and predict its dynamical behaviour such as in astrophysical accretion, you are either implicitly or explicitly providing additional postulates independent of Einstein equations and other known physics in general. 
I have been poking around the field of exact solutions to Einstein equations to tell you with relative certainty that there is really no prescription that would allow to give you a unique, covariant prescription for the behavior of all known naked singularities. The reason for that is that there is simply too many types of them - spacelike, timelike, null, directional, vacuum, nonvacuum, with various degree of divergence and dimensionality. So the postulates are typically done on an ad hoc, case to case basis.
So, addressing your question - you can really postulate anything to happen. You can postulate that the naked singularity will be annihilated in a burst of photons once colliding with the antimatter. However, you can also postulate the collision will produce a herd of beautiful unicorns that go and radiate love particles throughout the Universe. 
