Nature of a straight line in curved space

[Atom Man]

I've read that, because of the curvature of the universe, light going in a "straight line" would, given enough time, end up where it started. Now, I know this is impossible to do, but imagine if we had a wire making machine that could, for the sake of this thought experiment, make wire really, really fast. Ignoring the length of time it would take - would it also end up where it started so that the front end could connect to the back end, resulting in an actual loop of wire in some sense. Is there some abstract mathematical perspective from which it would be "seen" curving back on itself? I'm afraid - and I'm probably not the only one - I keep imagining it going in a big circle, but I know that can't be right! Any thoughts?

[Mordred]

photon sphere of a Bh just outside the event horizon can cause circular looped spacetime null geodesics

[pavelcherepan]

I think it's generally accepted at the moment that on a large scale the space-time is more or less flat, and in order for the light to come back to it's source curvature of space-time must exist.