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In general relativity, gravitational collapse of matter fields ends with theformation of a spacetime singularity, where the matter density becomes infiniteand standard physics breaks down. According to the weak cosmic censorshipconjecture, singularities produced in the gravitational collapse cannot be seenby distant observers and must be hidden within black holes. The validity ofthis conjecture is still controversial and at present we cannot exclude thatnaked singularities can be created in our Universe from regular initial data.In this paper, we study the radiation emitted by a collapsing cloud of dust andcheck whether it is possible to distinguish the birth of a black hole from theone of a naked singularity. In our simple dust model, we find that theproperties of the radiation emitted in the two scenarios is qualitativelysimilar. That suggests that observational tests of the cosmic censorshipconjecture may be very difficult, even in principle.

Can we observationally test the weak cosmic censorship conjecture?