I'm not sure if this belongs here or in Cosmology - possibly either would do, I think. I was reading the thread about open/closed/flat universes that's currently ongoing in Cosmology, and a related question occurred to me. According to post #7 you can have geometrically flat universes that are finite and unbounded if they have a non-trivial topology, such as a torus. Fair enough. Could someone explain the resolution to the twin paradox in this environment? It seems to me that I could sync watches with my twin as I pass him at constant velocity, circumnavigate the closed universe and return without having accelerated in either a proper or coordinate sense, since the geometry is flat. Appreciating that there's ten thousand twin paradox threads here I had a quick search. This one seems to me to be saying that a flat FLRW spacetime is not a flat spacetime in the Minkowski sense of the word. I'm not sure if I've understood that right, though. What don't I understand? For some context, I took a course in GR about fifteen years ago and remember not a lot and I'm currently on my second time through the first chapter of Carroll's lecture notes. "A lot" is a correct answer, but some precision would be appreciated.