Asklemmy

Hm, I don't think the "gravitational force" (as in the thing that pulls you towards the Earth) is a result of a gravitational wave; rather it is a result of you being in a static vector field. Gravitational waves are waves that travel through that field, e.g. the stuff that LIGO is measuring.

I've tried thinking about how it would work with portals. The problem is that the definition for gravitational field is g = -∇Φ where gravitational potential Φ(x) = ∑~i~(-G·m~i~)/||x - x~i~||, which depends on there being a single unambiguous "distance between two points" (x and x~i~ in this case). But think about two points on the opposite sides of one "portal entrance" (e.g. imagine a portal entrance on a wall in front of you, with your friend on the other side of that wall). What is the distance between you and your friend now? If we're to say it's the same as it was without a portal, then (1) we get straight back to our problems with energy conservation, (2) there is no physical path between you and your friend that matches this distance as there's a rift in space on that path. It would also be weird to conclude that it's infinity - you can just go around the wall in our example and be right next to your friend. So we almost have to conclude that the shortest path would have to go around the portal somehow. Let's just say that it would be the length of the shortest path around the portal. By the formulae for the gravitational field, this means that the gravity will pull you towards the shortest path to Earth's center. If you placed one portal on the surface of Earth (let's assume that the center of Earth is sufficiently far away that the gravitational field can be approximated as uniform in direction and magnitude) and another one somewhere far-far away in deep space (where let's say that gravitational field is 0 for simplicity) it would look something like this:

Note how while the gravitational potential (Φ) is defined along the red line, the gravitational field would be undefined as there would be no gradient in the gravitational potential.

Now let's try thinking what would happen on the other side. I'll assume that our portals are just flattened wormholes with short throats. Thus we'll just assume that portal entrances are actually "two-sided" (e.g. if they are just floating in your room, you can walk around them and see whatever is around the other portal at all times), and that the distance between them is 0 (let's not think about how that works for now). Now the distance between an object on "one side" of first portal entrance and "the other side" of another portal entrance is even more messed up - I think the shortest path would technically be one that travels from first object to one of the "edges" of the first portal entrance and then from the corresponding edge of the second portal entrance to the second object. Thus the gravitational field around the other portal would look like this (I've added eyes to clarify how I've linked up portal sides):

The red line once again means that the gravitational field there is undefined.

Whew, it's complicated, right?

Now, let's put the second portal close to the first one. Note that I'm assuming here that only the shortest distance to the center of the earth matters.

The two red lines from before now overlap, and there's another one - there's no gradient when the distance to the blue portal and to the earth is the same. It'd actually be longer than what I've drawn, and some sort of parabola in those areas, but I'm too lazy to do that. Hanging in the middle of that red cross would be a weird feeling - your top half would feel as though you're hanging upside down, while your bottom half would feel normal, and your arms and legs would be pulled in slightly different directions.

Although, I think that Newtonian definitions of gravity are playing tricks on us here. We should probably try using general relativity instead, but I am too tired to even attempt that right now, and I'd probably fail given that the fields involved there are a lot more complicated.