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<blockquote data-quote="Umbran" data-source="post: 6638886" data-attributes="member: 177">My understanding is that most solutions are unstable, unless you apply exotic matter to stabilize them.There are a class of solutions in 5+D space that may be stable without exotic matter - they may be stabilized by quantum effects. You hit upon the same basic idea with, &quot;The whole thing could just be a funny-shaped dimple on a single spacetime.&quot;I think it may be more clear to say it that it doesn't match the colloquial conception of a wormhole unless it makes the spacetime to be multiply connected (as opposed to simply connected, in a topological sense).&nbsp; Leave out the singularities like black holes, and if the space with the wormhole is still simply connected, that wormhole is just an oddly shaped dimple, as you put it.&nbsp; The wormhole may locally have different curvature than the rest of the spacetime, but from a practical standpoint... who cares?&nbsp; The question becomes very important when you start considering artificially creating a wormhole.&nbsp; A natural wormhole, as you've described them, is really just an area with slightly different curvature between two more normallly curved regions - one can imagine those developing naturally as the spacetime originally formed.But, when you consider an artificial wormhole - if you cannot connect to your own spacetime, then you must connect to another one - and then the question of how that can be possible when that other spacetime cannot be assumed to have similar properties, becomes a bigger question.&nbsp; We could find that even if we have exotic matter, we cannot create such a thing because there's nothing compatible to connect to!</blockquote>

[QUOTE="Umbran, post: 6638886, member: 177"] My understanding is that most solutions are unstable, unless you apply exotic matter to stabilize them. There are a class of solutions in 5+D space that may be stable without exotic matter - they may be stabilized by quantum effects. You hit upon the same basic idea with, "The whole thing could just be a funny-shaped dimple on a single spacetime." I think it may be more clear to say it that it doesn't match the colloquial conception of a wormhole unless it makes the spacetime to be multiply connected (as opposed to simply connected, in a topological sense). Leave out the singularities like black holes, and if the space with the wormhole is still simply connected, that wormhole is just an oddly shaped dimple, as you put it. The wormhole may locally have different curvature than the rest of the spacetime, but from a practical standpoint... who cares? The question becomes very important when you start considering artificially creating a wormhole. A natural wormhole, as you've described them, is really just an area with slightly different curvature between two more normallly curved regions - one can imagine those developing naturally as the spacetime originally formed. But, when you consider an artificial wormhole - if you cannot connect to your own spacetime, then you must connect to another one - and then the question of how that can be possible when that other spacetime cannot be assumed to have similar properties, becomes a bigger question. We could find that even if we have exotic matter, we cannot create such a thing because there's nothing compatible to connect to! [/QUOTE]

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