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.
Gonna hijack this post to ask a somewhat related but possibly stupid question, would it be possible that instead of a singularity there happened to be a region of space with non-negligible size (ie, not a point sized region) that acted like a well instead? Things could “fall” into that well and not be able to escape, but it’s not like everything in the well is at a single point.