Closed timelike curve

A closed timelike curve is a loop in space and time. Imagine a snake, the head of the snake is the starting point and the tail is the end point. Now, instead of thinking of the snake as just one line, imagine that the snake's tail is connected to its head. That's what a closed timelike curve is—it is a loop in space-time. So when you start at one point in space and time, you can travel around the loop and eventually you'll end up back at the same point you started, only in a different time! It's like a time machine!