Naked singularity
The existence of naked singularities is a very important topic in physics, because it would mean we could actually see phenomena made by black holes that we wouldn't be able to see otherwise. In addition, naked singularities would pose big problems for general relativity, since scientists still have not figured out a working idea for what happens to space-time in and around a black hole. Quantum mechanics, the main other scientific theory scientists turn to in physics, is also unable to explain how space-time would behave in such a situation.