The famous mathematician Kurt Gödel was a friend and neighbor of Albert Einstein at Princeton. And he became incredibly curious about Einstein's general theory of relativity, which was and still is our modern formulation of the force of gravity, and this theory relates the existence of matter and energy to the curvature of space and time, and then relates that curvature and warping to the behavior of matter and energy.
Gödel was curious about whether relativity could allow time travel into the past. Einstein's theory is claimed to be the ultimate framework for the nature of space and time, and as far as we know, time travel into the past is forbidden. So Gödel considered that general relativity should automatically prevent it.
Gödel discovered that general relativity fits perfectly with time travel into the past. The trick is to move the universe.
Gödel built a relatively simple, artificial universe model to prove his point. This universe rotates and contains only one component. It is a negative cosmic constant that resists the centrifugal force of rotation to keep the universe steady.
Gödel found that if you follow a certain path in this rotating universe, you may end up in your past. And you'd have to travel incredibly far, billions of light-years long, to do that.
As you travel, you will be trapped in the rotation of the universe. This is not just a rotation of things in the universe, but of both space and time. In essence, the rotation of the universe would alter your possible paths forward so severely that they would return to where they began.
You will embark on your journey, never traveling faster than the speed of light, and find yourself back where you started but in your past. The possibility of traveling back in time creates paradoxes and violates our understanding of causation. Fortunately, all observations indicate that the universe does not rotate, so we are protected from Gödel's problem of retrograde time travel.
But it remains a mystery to this day why general relativity is compatible with this seemingly impossible phenomenon. Gödel used the example of a spinning universe to argue that general relativity is incomplete, and he may be right.