Could the equator of a world be a closed-time like loop?

Most works of fiction have quite imaginative views of time travel. Mighty machines that teleport in time instead of space. Gaping portals in space that take you to another time. Mystical beings with a special power to move freely in time, sometimes taking a mortal companion.

Physicists, on the other hand, sometimes have different ideas. Willem Stockum, for example, showed that general relativity is consistent with a type of time travel where you walk in a circle and end up in the past, no machines, portals, or mystical powers necessary. Okay, you might need to run depending on how big the closed time-like curve is. GÃ¶del also studied this type of time travel.

My question is if a world's equator could be a closed time-like curve, making the first person to go around the world (via the equator) also the first time traveler.

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Could the equator of a world be a closed-time like loop?

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