Whoa! I love some of these olde threads! :-D
If anyonez still readin' here's another opinion:
Re: ""Einstein's general relativity says no, the fabric of space cannot tear."
* You shouldn't read pop sci literature in such a serious way. GR does not say any such thing! GR ASSUMES a Riemannian geometry. It
cannot therefore be said to predict spacetime is smooth. Greene would know this, but presummably was writing for a lay readership and so did not quibble about such nuances.
* In reply to,
...can't you just as easily have a metric on a manifold with a boundary?
Yes, that's perfectly ok. Far from such boundaries GR would be recovered one expects. In fact, a black hole is essentially such a simple point boundary, so we already know how to handle this type of topological defect in GR. How? Ignore it - as most textbooks do! Haha! ;-D
Textbooks tell us that GR "blows up" or becomes unphysical for black hole singularities. This may well be true, but you could always argue that GR doesn't become unphysical, in fact it is still entirely fine as a classical theory, it's just that it could be said to predict a point-like tear in spacetime = the singularity, which is now "outside" the physical universe, hence can be ignored. Only the effects of the singularity on the surrounding spacetime are important and physical.
Maybe I'm showing my bias, but I've always thought it silly of people to say GR is incomplete because it predicts a divergent curvature and mass-energy density in a black hole. I don't think there is anything wrong with infinities appearing, provided they are appropriately handled.
Having said that, I suppose a putative quantum gravity theory would have other things to say about spacetime tearing and so forth, a la the foamy spacetime picture - it could be interpreted perhaps as a massive amount of tearing! (As previous posts have suggested in other terms.)
