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Very good. The problem is that singularities are quantum objects. Quantum physics works nothing like classical physics.
For example, in the case of perpetually falling singularities, would they just quantum tunnel into each other? Or would singularities even exist? According to general relativity, singularities are a sphere that never stops being compressed due to its own gravity. What happens when this sphere hits a diameter smaller than Plank's length? Does the universe take a screenshot? The point is, we have absolutely no clue about what's happening here.
To understand the above, we would first need to understand how gravity works at the quantum level, which we don't. Why? Gravity is incredibly weak. Studying it is thus, very hard.
I was wondering today if singularities might actually be the purest form of "nothing" and the mass of a blackhole around that void is what is keeping that void from collapsing, kind of like a massive traffic jam. The space would have to be perfectly empty: No vacuum energy, no gravity, no fields of any kind.
Yes, this is a silly idea and just a weird thought experiment, TBH.
However, it's much more easy to visualize than a traditional infinite singularity since it can be rationalized in a simple 3D space... It's just a ball of nothing.
Hell, even if the void was the size of a pinhead, the entire force of the universe would be "squeezing it", trying to move energy into a space that contained none.
Ok, that probably broke a few hundred thousand universal rules of physics, but it's easy to speculate about something we can't see or study.