Traditional black holes, as predicted by Albert Einstein's theory of General Relativity, contain what are known as singularities, i.e., points where the laws of physics break down. Identifying how singularities are resolved in the context of quantum gravity is one of the fundamental problems in theoretical physics.
Nobody really thinks singularities exist. It’s only what comes out from our math. That’s also how we know our math is wrong, we’re just not sure yet how to do it better.