: : : Until a theory of quantum gravity is developed there isn't much other than speculation as to what a singularity is or even whether they actually exist.

: Vafa of Harvard developed the first quantum gravity of black holes some years ago. With it he was able to derive the entropy of a black hole from first quantum principles. : Actually, quantum theories abound. The problem is that we have no way of knowing if they are correct and that situation may go on forever.

You must be referring to string theory. All other quantum gravity theories are plagued by infinities. And it will be decades, if ever, before string theory can be fully developed