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I have always been fascinated by wormholes. Wherever I read about them, there was this thing that a wormhole sort of connects two points of space. Many books compare wormholes as connecting tubes. My question was that why can the wormhole not have three (or maybe even more) ends? Why cant we have sort of junctions in a wormhole? Would this enable a person wanting to create wormholes to let others travel through it? (by warping it in one direction by a person in one end and in the other direction by another person in another end, effectively cancelling each others' effects and making the wormhole traversable by the remaining ends) This question is not part of some theory or anything, it's just an idea I had. I would really appreciate if my idea were to be approved (or even disproved) by someone. i just need to clear my mind.

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It is very possible to have a junction of wormholes, but this is actually just equivalent to two wormholes.

There isn't really any good rigorous definition of a wormhole that covers all salient cases, but the one I tend to use is that, given a (not necessarily connected) spacetime manifold $\mathcal M$, a wormhole corresponds to the removal of two hypersurfaces along a spacelike hypersurface of the manifold which are then joined together, in such a way that the joint is small in some sense (ie the wormhole has a throat).

In other words, you cut out two regions of space and then connect them. If you consider the case of a wormhole with more than one end, this is actually just a single wormhole, plus another wormhole connecting a region inside the throat to a region on the spacetime manifold. It's not a terribly more appealing result because the energy requirements for such a system are always superior to that of a single wormhole (cf. Hawking's 92 paper for instance).

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