alt Hacker News>The fact that both have the same name
They don't just have the same name, they are the same thing.
A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.
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Even without quantum mechanics, black holes are trouble:
Approximately everything in nature rotates. Including black holes. Schwarzschild blockholes do not rotate. Rotating black holes are much more complicated and don't necessarily shield their singularity behind an event horizon.
> The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions.
How is this any different than classical? Isn't it still just an ~impossibility hidden behind an event horizon in either model?
We don't actually know if a black hole has an inside. Some theories/hypotheses say spacetime just stops at the event horizon.
OSM - slight generalization of Schwarzshild BH, where you take evolving spherically-symmetric mass distribution instead of point mass - shows that point singularity in the middle can be naked (aka observable), so it's not just QM that causes worms...
https://en.wikipedia.org/wiki/Oppenheimer–Snyder_model