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I have a setting in which there are nine planets in star systems scattered across the galaxy, linked together by some being or intelligence capable of manipulating spacetime. The current inhabitants of these planets have only cursory knowledge of how this came to be, but this arrangement is central to the setting; their technology and spaceflight capabilities are perhaps one or two centuries further along than our own, but they must be able to travel between these planets, even though they are separated by many light years.

The only way this arrangement is possible is through a wormhole network. I considered how wormholes are typically imagined, as spherical regions of space, which would be placed in these planets' star systems. But I'd like to take it a step further; I want the inhabitants to be restricted to the nine planets (and their moons). In other words, the planets will exist (or appear to exist) in the context of their star system and neighboring planets, but when the inhabitants cross a certain threshold (possibly the Hill radius?), they are transported to one of the other linked planets, or more likely a central hub linking all nine nodes. This cannot be achieved by wormholes as they are typically imagined. This is where the dilemma arises.

I have looked into various topics that may have the pieces necessary in explaining my setting, such as:

  • Non-orientable wormholes / Alice handles
  • Thin-shell wormholes
  • Manifolds; embedding; immersion
  • Brane cosmology
  • "Bubble universes"; multiverse theory

I must admit, however, that these topics quickly become extremely technical, and I have trouble applying them for my purposes.

Could the wormhole connection take a different shape than a sphere that is accessed from the outside? Could it be in the form of a membrane, somehow anchored to a planet's gravity well, that is accessed from inside? Could it somehow be embedded in a more complex topology, possibly a higher-dimensional manifold? I know that any solution will be theoretical, and I don't need a rigorous mathematical formula to explain it for the purposes of my story. But I do want there to be some logic behind it, rather than going the route of a magical portal system.

Is there a wormhole topology that makes sense for the setting I've described, in a way that allows the planets to locally appear to be in orbit around their stars, while being linked to the other planets? Note: If the solution requires that the planets lay in separate parallel universes, or something along those lines, I'm quite willing to accept that.

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    $\begingroup$ Please bear in mind that you're treating wormholes (and multiple dimensions, parallel universes, etc.) - and your expectations for an answer - as if they're real. Reality is that they're theories with a lot of mathematics behind them but no proof (yet) that they exist. Without empirical evidence, mathematics can be wrong. So when you think science-based, please keep in mind that answers will tend to reflect variations on the very mathematical theories you've been examining. There are limits to science as we understand it today. $\endgroup$
    – JBH
    Oct 15, 2023 at 18:59
  • $\begingroup$ We have a few questions that might interest you. They're not directly on-topic, but talk about sub-subjects that I believe are relevant to your research. (1) Can I map the location of my convenient store inside a wormhole? (2) [Can we make a wormhole inside another wormhole?](Can we make a wormhole inside another wormhole?) $\endgroup$
    – JBH
    Oct 15, 2023 at 19:07
  • $\begingroup$ Finally, let me set up one problem that's usually ignored with wormholes. Things move in the universe. Planets, start, galaxies... wormholes.... or maybe the wormholes don't (check out this Q on Physics.SE). You'll likely ignore this, too, but good old Sol is moving through space at an estimated 12,000 km/hr. That doesn't sound like much, but in 10 years the wormhole could be 1 billion km further away than it started. That's almost the distance of Saturn from the Sun. $\endgroup$
    – JBH
    Oct 15, 2023 at 19:13
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    $\begingroup$ Oh, and the second link in the comment above is Can we make a wormhole inside another wormhole? $\endgroup$
    – JBH
    Oct 15, 2023 at 19:14
  • $\begingroup$ @JBH , on your 3rd comment you cant make such general statements. It is also important to note that a Wormhole cant be static relative to everything else. Most metrics i am aware of can orbit another gravitational body and would just get dragged along. Some of the earlier ones might not though. $\endgroup$
    – ErikHall
    Oct 16, 2023 at 16:26

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If i understand you correctly, you want a shell around each Solar System which, once crossed, acts like a omnidirectional wormhole connecting all Systems to one central location. In essence, if fly in a random direction away from a Systems star, eventually i will hit the perimeter and be transported to the central hub.

Having done quiet a lot of work in General Relativity, mainly regarding Kerr Black Holes, i am not familiar with a Metric which describes such a spacetime. However, i dont think the geometry is impossible because mathematically valid metrics such as the famous Alcubierre one do describe a bubble enveloping a region of spacetime. Just based on this i think there should be a "Alcubierre Wormhole".

The tricky part is connecting many of these Solar System encompassing structures to the same hub. It would in essence require one part of the "Alcubierre Wormhole" to look different, than the other. If the structure at a solar system is a big sphere, then it cant be the same structure at the destination, or you have overlapping structures. I am just aware of one such metric which imagines different spacetimes for two ends of the same structure, which is a Kerr Black Holes Ringularity, which some hypnotize to lead to a White Hole (which is BS if you ask me). Outside of this, i dont think there is any metric you could base this on.

One idea might be the Solar System scale "Alcubierre Wormhole" represents the inside of a sphere, which orbits at the destination. In essence, when you fly through the Solar System wormhole you emerge on the outside, appearing to fly away from what looks like a spherical Wormhole. So the "Inside" of the Wormhole is enveloping the Solar System, and the "outside" is at the destination. This way you just have a bunch of spherical wormholes at the hub. Though note, the lensing these things create would look nothing like a conventional Wormhole. But those would all have to be the size of their respective solar system. Though you might be able to make them smaller. Like this; enter image description here

At the end of the day, you wont get a good answer here because the math require to derive something like this would take decades. And at least as far as we know, GR does not require extra universes or anything along those lines. And what you imagine is probably geometrically possible, if unholy energy expensive. But just in terms of Geometry, yeah this should work. Though make sure to mention these are Geometric contraptions. So they have no Time dependency, meaning they dont create a gravitational pull.

EDIT

Following OPs clarification ill amend my answer. As they have stated, this setup is naturally also applicable to a single planet.

The Propagation of light and gravity is more difficult to imagine, because it depends on the geometry which i cannot know. However, we can imagine the simplest possible case. A geodesic the a straight line, through curved space. We may imagine the "Alcubierre Wormhole" preserves Angles. This means, in essence, the direction you enter at, is the same as the one you exit; enter image description here

Here you can kind of see how that might look, despite the internal geometry warping the path, the exit angle is the same. Such Metrics do exist, specially Wormhole ones which have no lensing. Accordingly, this Wormhole type contraption would appear like the normal night sky. And from the outside it may just look like a portal since light passes straight through with no alteration to the trajectory.

Gravity would presumably act in a more complex way. My gut feeling is that Gravity, or the curvature of spacetime, would be preserved by the Wormhole as well. So However, it would be a weird well; enter image description here

If the Gravitational field of the planet passes through the Wormhole, then we would expect it to just continue on the outside, but with an apparent cutoff right on the edge. Of course this is not a true cutoff but rather just where we change from Outside to Inside of the Wormhole.

If Gravity passes through, then presumably all the Wormholes have to be in orbit around the central hub. Though depending on the scale the gravitational influence may be so small it is hard to notice.

The alternative is that the Metric of our Fictional "Alcubierre Wormhole" negates ambient gravitational wells. But that opens a whole new can of worms. So i would just leave it by saying Gravity passes through the Wormhole like anything else, but due to the scale involved it is just not super concerning.

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  • $\begingroup$ I was actually thinking of a shell around individual planets, rather than entire solar systems. But I see no reason why the setup you described could not be scaled down to achieve this. I had not considered passing from the inside of a spherical shell to the outside at the hub, which greatly simplifies things such as orientation. My concern is how each parent sun's light, energy, and gravitational pull would translate across the wormhole boundary, and how this would affect the environment at both sides (on each planet and at the hub). $\endgroup$ Oct 15, 2023 at 18:41
  • $\begingroup$ @sevenempest i edited my answer $\endgroup$
    – ErikHall
    Oct 15, 2023 at 19:04
  • $\begingroup$ Light passing through without being distorted is ideal on the planets' end, though I'm wondering if the wormhole can be permeable solely this way. It seems contradictory for me to say that matter can pass both ways, while light only crosses one way (i.e. the surroundings of the hub is never visible from the planets). I am also curious as to the "can of worms" you reference in the last paragraph, if the wormhole metric negated gravity wells. Even if the wormhole encompassed the entire Hill sphere of each planet, it seems each sun's gravity well would pose problems at the hub. $\endgroup$ Oct 17, 2023 at 0:26
  • $\begingroup$ It may be a moot point, since we're imagining an arbitrary metric for a specific wormhole setup. I feared that when I asked the question, as the subject matter is theoretical and highly complex. But I can't imagine a different way of connecting planets from nine separate systems, in a way that limits the focus to these nine planets alone (as I'd expect such a society to travel to the nine worlds' intra-system neighbors as well, which I wish to completely ignore). $\endgroup$ Oct 17, 2023 at 0:40
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    $\begingroup$ I'll have to look further into these metrics you've referenced. That is an interesting thought, as I imagine the Hub to be a void, with nothing observable but the wormholes. Though it may be impossible, I'll continue with this geometry, as there is at least some symmetry and order to it. Your mention of massive and massless particles also sparked an idea. $\endgroup$ Oct 20, 2023 at 2:40
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Or you could go with something like this: Their ability to travel to other star systems instantaneously is actually a repressed mind-body ability (given by the entity) that they are unaware of and cannot control (yet). It simply activates at some distance from the planet's surface (magnetic field or gravity sensing). They therefore imagine the method of this travel to be based on some sort of wormhole shell that they cannot even see or explain.

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  • $\begingroup$ That is an interesting alternative. One potential problem I see is that there are spacecraft of many sizes crossing between the systems too, so this ability would somehow have to translate to a person's surroundings, not just their body. $\endgroup$ Oct 23, 2023 at 21:15
  • $\begingroup$ Yeah, I thought about the spaceships, and just assumed they would teleport along with the people, (just as other non organic matter such as their clothing would). But maybe the ships could be part biological/organic. Or maybe only some of the people have this ability (let's call them pilots) and they connect to the ships with a neural interface. $\endgroup$ Oct 24, 2023 at 9:03
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The simple way to do this is to let the civilisations explore their individual solar systems. However, the wormholes are their only way of reaching other stars. This is rather easy, because interstellar space is huge and none of the ways of traversing it rapidly which science fiction resorts to are actually physically plausible.

So the nine civilisations get to communicate, and have travel and trade, at a very high cost, but until they make some huge theoretical breakthrough, they cannot create more wormholes. They probably will make that breakthrough eventually, because they know that it's possible, but as the author, you can defer that until it suits you.

In that situation, their individual solar systems will not be the focus of the civilisations. They may use them for resource extraction, but that's about all.

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  • $\begingroup$ True, it would be an overall simpler setup if it were more typical wormholes placed within otherwise normal solar systems. I'm curious as to your final point, about these particular planets remaining the focus even if the entire system was open to them. One detail I didn't include was that not all of the planets are habitable; for instance, one is highly volcanic due to extreme tides, one is a desiccated carbon world around a white dwarf, etc. Without some driver to push them to settle/industrialize these planets, I figured they'd probably settle the asteroids instead. $\endgroup$ Oct 23, 2023 at 21:10
  • $\begingroup$ @sevenempest: "One detail I didn't include was that not all of the planets are habitable" Well, if you don't mention these things we have no way to guess them, do we? You gave the impression that the nine planets were all friendly. Were that the case, there would be little reason to settle the asteroids. $\endgroup$ Oct 23, 2023 at 21:19
  • $\begingroup$ I see how it could have been interpreted that way, apologies. I didn't include details about the planets because I thought it might distract from the focus of the question, the wormhole network. $\endgroup$ Oct 23, 2023 at 21:33

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