I know very little about general relativity. I know that objects with mass bend space. How would you arrange objects to get a wormhole? My main problem is that I do not understand how you would change the topology of space to make the hole part in the wormhole.
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There's nothing that you might call "concrete", but there are some suggestions. First, a reference suggestion: Kip Thorne's "Black holes and time warps" is a very approachable popular account of general relativity and many of its most interesting aspects. It's also generally quite accurate (though not always entirely up to date). Though Thorne's recent Nobel prize was for gravitational waves, he also did a lot of research on wormholes, so he's probably the world's leading authority on them.
In that book, you'll find him pointing out three possible ways to create a wormhole. The first is the quantum approach, which is entirely speculative, but cannot be ruled out:
Since the quantum foam is everywhere, it is tempting to imagine an infinitely advanced civilization reaching down into the quantum foam, finding in it a wormhole ..., and trying to grab that wormhole and enlarge it to classical size.
The exact method behind this, and even the suggestion that it could be possible in principle, is highly speculative. But for all we know, it could work. Nonetheless, Thorne quickly dispenses with this approach because it is so unknown.
He then moves on to the second approach, which we might call the classical-quantum strategy. Again, he appeals to an infinitely advanced civilization, suggesting that they could
warp and twist space on macroscopic scales (normal, human scales) so as to make a wormhole where previously none existed. It seems fairly obvious that, in order for such a strategy to succeed, one must tear two holes in space and sew them together. ...
Now, any such tearing of space produces, momentarily, at the point of the tear, a singularity of spacetime, that is, a sharp boundary at which spacetime ends; and since singularities are governed by the laws of quantum gravity, such a strategy for making wormholes is actually quantum mechanical, not classical.
Again, he begs off by pointing out that we don't understand quantum gravity. So he moves onto the third "perfectly classical way". Now, if the previous descriptions sounded vague, get ready. The only concrete thing that can be said about this approach is that
while the construction is going on, it must be possible to travel backward in time, as well as forward; the "machinery" that does the construction, whatever it might be, must function briefly as a time machine that carries things from late moments of the construction back to early moments (but not back to moments before the construction began).
He also says
I wish that I could draw a simple, clear picture to show how this smooth creation of a wormhole is accomplished; unfortunately, I cannot.
From my cursory reading of the literature, I think this is because no such creation has really been devised in detail, even assuming some technology vastly beyond our powers (besides the time machine).
Also note that Thorne's research showed that a wormhole is only stable (and therefore can only be held open) if it is "threaded with exotic material." Again, we don't know how that could be done. All that Thorne is talking about here is a proof that if such a thing can be done, then it requires a time machine.
