1. The Closed Timelike Curve

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A closed timelike curve (sometimes abbreviated CTC) is a theoretical solution to the general field equations of the theory of general relativity. In a closed timelike curve, the worldline of an object through spacetime follows a curious path where it eventually returns to the exact same coordinates in space and time that it was at previously.

Normally, a closed timelike curve comes out of the equations through something called frame dragging, where a massive object or intense gravitational field moves and literally "drags" spacetime along with it. Many results that allow for a closed timelike curve involve a black hole, which allows for a singularity in the normally smooth fabric of spacetime and often results in a wormhole.

One key thing about a closed timelike curve is that it is generally thought the worldline of the object following this curve doesn't change as a result of following the curve. That is to say, the worldline is closed (it loops back on itself and becomes the original timeline), but that has "always" been the case. >>>>>>>>>>>>>>>>4 >>>8 >>>>>>>>>>° >>>>>>>>>>>>>>>>>23 >>>>>>>>>' >>>>>>>5 >>>>>>>>>>>>>>>>>>>>>>>4 >>. >>>>>>>>>>>>>>>>>>>>>>>>>>>7 >>>>3 >>>>>>>>>>>>>>3 >>>>>>>>>>>>>>>>>>>2 >>>>>>>>>>'' >>>>N >>>>>>>>9 >>>>>>>>>>>>>>>>>>>>>° >>>>>>>>5 >>>>>>>>9 >>>>>>>>>>>>>>>>>>>' >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>3 >>>>>>>>>>3 >. >>>1 >>>>>>>>>>>>>>>>>>3 >>>>>>3 >>>>>>>>>2 >>>>>>>>>>>>>>>'' >>>>E SOLVED