Monday 1 June 2020

general relativity - Building a wormhole


We regularly get questions about wormholes on this site. See for example Negative Energy and Wormholes and How would you connect a destination to a wormhole from your starting point to travel through it?. Various wormhole solutions are known, of which my favourite is Matt Visser's wormhole because it's closest to what every schoolboy (including myself many decades ago) thinks of as the archetypal wormhole.


The trouble is that Visser has pulled the same trick as Alcubierre of starting with the required (local) geometry and working out what stress-energy tensor is required to create it. So Visser can tell us that if we arrange exotic string along the edges of a cube the spacetime geometry will locally look like a wormhole, but we know nothing about what two regions of spacetime are connected.



My question is this: suppose I construct a Visser wormhole by starting in Minkowksi spacetime with arbitrarily low densities of exotic matter and gradually assembling them into the edges of a cube, how would the spacetime curvature evolve as I did so?


I'm guessing that I would end up with something like Wheeler's bag of gold spacetime. So even though I would locally have something that looked like a wormhole it wouldn't lead anywhere interesting - just to the inside of the bag. I'm also guessing that my question has no answer because it's too hard to do any remotely rigorous calculation. Still, if anyone does know of such calculations or can point me to references I would be most interested.




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