Twin paradox with portals connecting a stationary station and moving spaceship

[JesseM]

Isn't all this stuff just speculation though?

Yes, it's speculative, but it's not just an arbitrary sci-fi fantasy (like "wouldn't it be cool if there was some way to make a portal connecting different places"), traversable wormholes are valid solutions to the equations of general relativity, and thus of interest to theoretical physicists exploring the consequence of the theory. Whether they are possible in the real world depends on whether the right type of "exotic matter" is possible (certain results from quantum theory like the "Casimir effect" suggest there's a good chance it is, but it's definitely not settled, see here), and also on whether there would be any process that could give rise to one in a region of space where one hadn't already existed since the Big Bang.

 

[SeventhSigma]

What would be an example of a wormhole being a "solution" to a GR equation?

 

[JesseM]

What would be an example of a wormhole being a "solution" to a GR equation?

I don't know what you mean by an "example", are you looking for the equations of a specific spacetime metric involving a wormhole? A solution just means a spacetime with a metric (describing a curved spacetime) and a matter field that satisfies the Einstein field equations (dealing with the relation between matter distribution and spacetime curvature) at every point in the spacetime. Anyway, the detailed equations for one such solution can be found in this paper, for example (the author also has a full textbook on the subject titled Lorentzian Wormholes)