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A black hole in GR seems to have a sharply defined radius. Of zero, that is since all the mass has been compressed into the infinitely dense center point. However, shouldn't the fuzziness of quantum mechanics destroy this well-defined shape before the absolute point is reached?

That is, how can the classical diagram of a black hole like a vortex exist when the sides of the vortex are quantum-close to each other?

So here's the quantum uncertainty I'm referring to. Pink is the quantum closeness one can have I suppose.enter image description here

Next, in respect to Jeremy Schirmer's answer, are you saying that within the event horizon space basically doesn't exist anymore? That's quite wild of a thing to say but in no way surprising when it comes to black holes.

enter image description here

Andres Salas
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People expect the singularity to not actually form, and for there to be some different structure to the object at distances where the curvature approaches $\frac{1}{\ell_{P}^{2}}$, where quantum gravitational effects should become important.

There are some other researchers that expect the spacetime to be cut off at the horizon of the black hole and there to be a boundary to spacetime there, and you thereby avoid having to ask questions about the singularity itself.

Zo the Relativist
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  • Second proposition: spacetime is deleted. How wild. I added a picture so see if I'm understanding what you're saying – Andres Salas Aug 05 '14 at 20:18
  • Although John Rennie's answer to this question seems to imply a very real singularity from the perspective of the faller. http://physics.stackexchange.com/questions/28228/why-is-matter-drawn-into-a-black-hole-not-condensed-into-a-single-point-within-t?rq=1 – Andres Salas Aug 05 '14 at 20:32
  • @AndresSalas: the answer of mine you refer to is a purely classical treatment, and the classical theory of general relativity does indeed predict singularities really form. Jerry's point is that we expect quantum theory to modify general relativity at very short distances, and we think the result will probably be that singularities do not form. – John Rennie Aug 06 '14 at 08:52
  • General relativity used to be very non-classical, an interesting name, I wonder what Einstein would think! TY for the clarity. Yes I'm glad the question was well-founded. Who knows what will happen around the planck length to an object falling within, poor singularity. @JohnRennie thanks – Andres Salas Aug 06 '14 at 14:46