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In one of the documentaries hosted by Morgan Freeman, a reference was made that just like an ordinary three-dimensional object like a ruler has scratches and cracks, in the same way there might be minuscule loops in space-time. My question is this: If many bodies of extremely high densities are brought close together, will it deform the space-time fabric and hence create a permanent loop in space-time that might be accessible if ever achieved?

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Are you asking about making a wormhole? See en.wikipedia.org/wiki/Wormhole for what a wormhole is. – John Rennie May 22 '12 at 18:03
What is a "rupture" in space time? The concept doesn't make sense to me. – Ron Maimon May 23 '12 at 6:08
Not exactly a wormhole, because that would imply that we are trying to enlarge an already existing rupture in space and time, whereas what I am referring to is creating a rupture only in time. However, an unintentional space rupture is possible if the objects of very superior densities are brought together. – Graviton May 23 '12 at 16:51
A rupture means a warp. I'm sure that you're familiar with the idea of a very massive object "warping" the space around it. When I say 'rupture', I mean that space-time is caused to distend to such an extent that it no longer exists in that portion. I would like to use the bed-cloth metaphor. If really sharp/heavy objects are placed on the cloth, it tends to tear, hence making a gap in the middle of its material which allows free transport between the two sides of the cloth. The same way, ruptured space-time should be able to provide this free gap between any two accessible ends. – Graviton May 23 '12 at 16:58
@argentocyanide: Space is not like a rubber sheet--- this is a bad analogy. You mean a jump point--- a surface where you jump as you cross somewhere else--- but this type of gluing is not distinguishable from nothing except to the extent that the effective 4d space is full of curvature. – Ron Maimon May 23 '12 at 20:05
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Spacetime is infinitely stretchable - in fact at the singularity in the centre of a black hole the spacetime curvature becomes infinite (though quantum gravity probably intervenes before the curvature actually becomes infinite). Spacetime cannot "snap" or "rupture" no matter how heavy the masses involved.

I can't think of anything in General Relativity that matches your description. Just possibly something like this may happen in quantum gravity. See http://en.wikipedia.org/wiki/Quantum_foam for more info, though note that the idea of a spacetime foam is purely speculative at the moment.

I believe string theory allows topology change to occur, and I suppose this could be viewed as a "tearing" of spacetime. However I don't know enough about this area to comment.

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Thanks @John Rennie, that answers my question, but gives rise to some new ones. How exactly would this 'topology change' be perceived by an observer? And in the link that you mentioned, it says that the Uncertainty Principle allows energy to turn into matter, anti-matter, etc. but seeing that there is no energy involved, it doesn't seem justified. The singularity itself is an extreme concentration of mass, not energy. – Graviton May 24 '12 at 9:36
GR uses an object called the stress-energy tensor, which includes contributions from both matter and energy. So both matter and energy can curve spacetime. Actually the stress-energy tensor includes other things as well like momentum density, pressure and shear stress. See en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor for more details, though this is probably beyond the popular science level. – John Rennie May 24 '12 at 10:21
The topology change in string theory only happens at the string scale i.e. huge energies and tiny distances. If it could be perceived at all I think it would look like the quantum foam I've already mentioned. – John Rennie May 24 '12 at 10:22

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