Can Spacetime Fold Back On Itself?

Large masses cause spacetime to distort, which is why pmasses moving by them follow curved paths ororbits. Can a sufficentlt large mass cause the time dimension of spacetime to fold back on itself?
Could AD 2010 then be folded back to AD 1700 or so? That would be neat!

I don’t have my books with me here at home, so I can’t look up what’s known and not known about them; but what you’re talking about is called a “closed timelike curve” by those of us in the biz. They work much as you describe: in the presence of sufficently large masses and energies, situations can arise in which you can travel “forward in time” through spacetime and end up at the time & place you started at.

Most GR folks view closed timelike curves as something to be avoided if you’re trying to describe physical situation, and I have a vague recollection that under certain assumptions about the masses & energies you’re working with (things like “no negative masses allowed”), you can show that CTCs don’t arise. I’ll try to remember to post back here once I have a spare moment and my textbooks on hand (if another one of our local experts doesn’t beat me to it.)

This is correct, but I also can’t remember precisely what the nonnegativity condition is, off the top of my head.

As a consolation prize for the OP, though, I’ll mention that, in the standard coordinates used for black holes, inside the horizon t becomes a spacelike coordinate, while r becomes a timelike coordinate. So while you’re inside the hole, you can travel in “time” freely, but you’ll always, inexorably, get closer to the center, just like you’re always getting closer to tomorrow.