Can the fabric of space, or space-time, rip and tear? It would seem that the fabric can stretch, that it has some sort of elastic property. Does elasticity imply a tension at which it can rip or tear? Would that ripping tension be the tension of a string? Thanks.
If strings are the boundary of space created by space tearing, perhaps the violence of the tearing of the fabric of space is what sets the vibrational modes of the strings.
Are there any topological consideration for an expanding closed manifold to tear and form a boundary?
http://arxiv.org/abs/astro-ph/0302506 this site discuses the phantom energy model and the possibility that our end will a "big rip", i dont know about a string model for this end but then i know nothing about SF.
If there were no resistance to the expansion of the initial manifold, then the expansion would almost immediately accelerate to an infinite speed. So there must exist some mechanism to prevent instantaneous change in expansion rate. I'm wondering what topological properties might be involved. It seems as though there are two tendencies here, one is the tendency of the initial compact dimension to uncurl so that the curvature of space would flatten out, and the other is for points in space to adhear to one another (whatever adhear means, maybe some sort of elastic property). I can imagine a situation where the tendency for the curvature of space to flatten out might overcome the tendency of points in space to adhear to each other so that eventually tears in the fabric of space form. Might this all be due to one overall effect... I wonder if the tendency of points in space to adhear might be responsible for curvature to flatten out. I imagine some elastic material that is bent having a tendency to flatten out.
OR,... perhaps there is a positive divergence at every point of space (not in particles) that acts as a source of more space. Certainly the very first point of space was divergent since it expanded. I imagine that an outward pressure (of space) would have a tendency to make adjacent points travel in straight lines so that curled up space would flatten out. Does GR predict a positive divergence of space? Would such a divergence be proportional to the size of the universe? If the density of space can change, then it can become zero, right?
Brian Green, in his book, The Elegant Universe, page 263, says, "Einstein's general relativity says no, the fabric of space cannot tear. The equations of general relativity are firmly rooted in Riemannian geometry and, as we noted in the preceding chapter, this is a framework that analyzes the distortions in the distance relations between nearby locations in space. In order to speak meaningfully about these distance relations, the underlying mathematical formalism requires that the substrate of space is smooth -..." In other words, GR studies a metric on a manifold. My question is... can't you just as easily have a metric on a manifold with a boundary? If so, then that boundary can be distributed as well, can't it?
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, 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.)
KOSS, please don't post on the tail of old threads like this. It's referred to as necroposting, and it's frowned on here. -Ben