The reason that the heart of a black hole is called a "singularity" is because the word singularity is just shorthand for "the place where the math model breaks down and we don't know WHAT is/was going on". In other words, it is unknown just what is at the heart of a black hole since the math gives unphysical results. The hope/belief is that if/when we get a solid theory of quantum gravity we might get an answer to that question.