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Forget about wormhole-stabilizing fields and energies. Wheeler and Fuller's paper describe the expansion and subsequent collapse of a created wormhole. Essentially they describe a created wormhole as first growing to a maximum size, while also expanding all the space around it, and then collapsing whilst contracting all of space around it. (The paper is well worth the read)

From a Ricci flow perspective this makes sense. What happens however when space is expanding with time also (as measured in our own universe)? It would seem reasonable (from a purely qualitative view) to suppose that such an expanding metric would counteract or even halt the contracting space and collapse of wormholes (or other nontrivial topologies) at particular sizes (Given the Hubble value, probably VERY small).

Can anyone weigh in here? I'd like to tackle the problem from a more quantitative point of view.

This scheme might be best defined for a closed space, as the scale parameter is then uniquely defined. I couldn't help but find intriguing, the possibility of linking cosmological parameters to something that would probably end up being very small.

Before any input, I was thinking an approach utilizing Ricci solitons might be appropriate.

Qmechanic
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R. Rankin
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1 Answers1

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The expansion of the universe isn't a force. The closest you can get to an expanding vacuum in general relativity is a vacuum with a positive cosmological constant.

Fuller and Wheeler's paper only analyzed the maximally extended Schwarzschild black hole geometry. If you add a positive cosmological constant, you get a Schwarzschild-de Sitter black hole. It has the same nontraversable wormhole as the Schwarzschild black hole.

Nothing about their analysis extends to other wormhole types. They point out that it doesn't apply to the Nordström geometry (electrically charged), which theoretically contains traversable wormholes to an infinite number of other exterior regions. It also has no relevance to wormholes that use exotic matter.

Realistic black hole models don't have other exterior regions, reachable or not, and exotic-matter-stabilized wormholes probably can't exist in real life.

benrg
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  • "The closest you can get to an expanding vacuum in general relativity" you can have expanding Vacuum without cosmological constant, a closed expanding universe is a prime example, it will only expand for a finite time however. I'm not interested in traversable wormholes, more like wormholes describing particle like properties. – R. Rankin Sep 27 '22 at 19:36
  • I'm not interested in expanding space as a force, but rather just a counter to space's contraction around a wormhole collapsing (which we also wouldn't describe as a force) – R. Rankin Sep 27 '22 at 19:38
  • @R.Rankin A recollapsing closed universe isn't a vacuum: it has $4πG(ρ+p)=(\dot a/a)^2+k/a^2-\ddot a/a > 0$. If you put a black hole in the middle of that, then the FLRW matter will fall into it and it will expand. It's a complicated dynamical situation and I don't know what the geometry would look like. The FLRW matter isn't present in reality (see the first link in my answer), though you could still supply your own matter. There most likely aren't any full-Schwarzschild-geometry black holes to toss it into; gravitational collapse doesn't produce them. – benrg Sep 27 '22 at 21:09
  • Remember I'm trying to consider the matter as wormholes themselves. In your own words (second link in your answer): "FRW is essentially a bunch of Schwarzschild patches sewn together and then smoothed to remove the local bumps." Which are themselves all vacuum solutions – R. Rankin Sep 27 '22 at 23:00
  • But we could consider the spatially closed noncontracting "knifes edge balanced" or even flat FLRW universe, maybe that's more acceptable in this context? – R. Rankin Sep 27 '22 at 23:08
  • Please see related questions for more context https://physics.stackexchange.com/q/729307/2451 – R. Rankin Sep 27 '22 at 23:10
  • Apologies, the notion of considering the matter as tiny maximally extended Schwarschild metrics was not mentioned in my question. Essentially, I was wondering if they might stabilize in an expanding space full of them – R. Rankin Sep 27 '22 at 23:15
  • Sorry those words were from another answer of yours here: https://physics.stackexchange.com/questions/282165/schwarzschild-metric-in-expanding-universe – R. Rankin Sep 27 '22 at 23:23