Supermassive black hole Sagittarius A* is spinning nearly as fast as it can, dragging the very fabric of space-time with it and shaping the heart of the Milky Way.
That’s not known. Relativity predicts that they shrink to an infinitely dense singularity, but we don’t know that relativity is still applicable in that environment. They could shrink to a small but finite volume, or they could stay at uniform density within the sphere of the event horizon (which would make SMBHs less dense than water), or space could just stop at the event horizon and there wouldn’t even be an inside. And all those possibilities would look identical from the outside.
Black holes have infinite density, so they have a good start on breaking some rules.
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That’s not known. Relativity predicts that they shrink to an infinitely dense singularity, but we don’t know that relativity is still applicable in that environment. They could shrink to a small but finite volume, or they could stay at uniform density within the sphere of the event horizon (which would make SMBHs less dense than water), or space could just stop at the event horizon and there wouldn’t even be an inside. And all those possibilities would look identical from the outside.