Topology of an exotic wormhole network?

Question

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.

Answer 1

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;

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;

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;

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.

Answer 2

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.

Answer 3

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.