I assume the twin paradox from special relativity is well known. I wish to focus on the apparent symmetry of the problem: both observer seems to move away from each other, and then come back. Yet, the outcome is asymmetrical. That paradox is resolved because the travelling twin has to turn around at some point. Then he has to change inertial frames, or accelerate, and this means that the situation is not symmetric anymore.
What now if the "turn around" is not caused by an acceleration, but a "gravitational slingshot". Say, the traveling twin's trajectory passes by the graviational field of a couple of stars, freely falling, such that the twins just happen to end up in the same place after a while again. According to general relativity, both twins then remain in an inertial frame. Both see the other initially disappear with slowly ticking clocks, and later reappear from some other direction. All the while, they stayed at rest in their own reference frame. So the other twin must have aged less than themselves. The situation seems completely symmetric again. Of course, since they meet in the same point again, they cannot consider the other one younger from both perspectives.
What is the resolution?
I found this other thread which seems related: Symmetrical twin paradox This refers to a paper that claims that this is due to the fact that the topology of the space induces some preferred reference frame. I don't pretend to understand that paper, but I think it refers to a similar paradox obtained by assuming that the large-scale structure of the universe is spherical/cylindrical, or something like that, allowing one twin to travel "around". Surely it is possible to set up my above scenario with only a few local stars. So it seems strange to me that a local paradox should be solved by relying on a global topologically prefered frame.