I know that folding spacetime is completely possible, and i'm pretty sure that the answer i'm looking for is in Einstein's field equations. I just don't know enough about tensor calculus (yet) to figure this out for myself. So my question: how much energy is required to completely fold a certain portion of spacetime? for example, how much energy would be required to fold enough spacetime to travel 1 lightyear. I know cosmic strings have quite a bit of energy, and that if two cross just right we think that they will have enough energy to fold spacetime completely. If the answer is really in the field equations, could someone please go step by step? like i said, im not that familiar with tensor calculus yet but this question is really starting to bug me.
By folding i mean manipulating spacetime to the point where two seperate points in spacetime that are very far away, become very. picture a very long thin object with a huge amount of mass. it would bend spacetime to look like a "V" if you were looking perpendicular to the third spacial dimension. now, i want to fold it completely. making a "()" shape. this is one of the few ways we know to theoretically travel through time and teleport ect. By doing this, we are essentially bypassing all of the folded space. My question is, how much pure energy would be required, because it takes a lot more energy to manipulate spacetime than it does for mass.
You might want to start here: http://en.wikipedia.org/wiki/Wormhole If you look at the embedding diagram, you'll see two types of curvature: there's (1) the curvature of the cylindrical "fold" on the left, and (2) the curvature of the hourglass-shaped region connecting the top and bottom sheets. The type-1 curvature is extrinsic curvature, i.e., it doesn't really exist; it only seems to exist because of the way we draw the embedding diagram. So the literal answer to your question is zero. But the type-2 curvature is intrinsic, i.e., it really has detectable consequences. Googling shows people tossing around estimates of the energy involved that come out pretty stupendous, like an amount equal to all the energy our sun has ever produced. Another issue is that as far as anyone can tell, you need some exotic matter (matter with negative energy density) to stabilize the wormhole. As far as we know, that doesn't exist. Another issue is that objects traversing the wormhole might actually be destroyed by the intense radiation inside. If a wormhole did exist, it would also automatically be possible to use it as a time machine, so it would violate causality. There's a good discussion of this in the final chapter of Black Holes and Time Warps, by Thorne.