Everyone's knowledge obviously varies so I won't assume yours, but I'd invite you to closely study stars that form into neutron stars and then study neutron stars until you have a very good understanding of their evolution; I found them to be more interesting than black holes and one of the most extreme and large objects where a lot of quantum mechanics is needed to best understand them. In this process you'll learn about neutron star's various but inevitable transformations. And the more you learn about them, the more you'll understand black holes and the unanswered questions about them.

All of that said, here are two fun questions to consider in trying to answer your question:

Math is an extremely powerful tool but as we're unable to know the limits of physics within a black hole, this leaves us able to play with mathematical theories and often allows for infinities to arise - to renormalize or not to renormalize, that is the question? So then you must ask yourself where you want to draw the line: in what can be observed (including what neutron stars reveal about extreme gravitational bodies), or add the mathematical theories that can explain the internal workings of a black hole? Sure, I'll take interest in the latter but always remember it's just a mathematical theory and continue to have an open mind to new discoveries...