Anything that approaches infinity tends to be a problem scientifically and maybe mathematically. I have long suspected that matter might have a maximum density, making Black Holes not a point with infinite density but a tiny sphere. It seems plausible since our mathematics tends to break down when discussing singularities.
Perhaps Black Holes could spin so much, or have a high enough energy that these would counter the collapse? Maybe the time dilation becomes so great that it never becomes a point?
I am wondering if this is something that can be proved one way or the other using observations?
It might become 'solid' at the point where the gluons are pressed into the quarks, shoving all these particles into a TRUE solid, where the particles are totally crushed together and no space at all remains. I don't believe we could simulate that, because the energy required to compress quarks and gluons in such a way would be beyond our capacity to generate.
@Alondro77 We know that subatomic particles are fluctuations in Quantum Fields. Although we haven't defined a limit to the amount of energy that a Quantum Field can have at any particular point, it seems to me that there could be a limit where either it is not possible, or the field breaks, or it changes into something else.
I don't think that we know what the fields are made of and probably will never know, but there might be properties at higher energy levels or densities that we will never be able to test.