Is There a Singularity at the Center of a Black Hole?

We don't know what's going on inside a black hole. Matter has many ways to protect itself from collapsing. There might be something else quantum mechanical that matter can do to resist being compressed into a singularity. To know how that works, we'd have to have a theory of quantum gravity, which we just don't have. From the outside, it still just looks like a black hole because you can't see beyond the event horizon.