He discovered a solution to Einstein's field equations that permits closed timelike curves if the universe is rotating. http://en.wikipedia.org/wiki/Godel_metr

He discovered a solution to Einstein's field equations that permits closed timelike curves if the universe is rotating. http://en.wikipedia.org/wiki/Godel_metric http://en.wikipedia.org/wiki/Godel_metric "This solution has many strange properties, discussed below, in particular the existence of closed timelike curves which would allow for a form of time travel in the type of universe described by the solution. Its definition is somewhat artificial (the value of the cosmological constant must be carefully chosen to match the density of the dust grains), but this spacetime is regarded as an important pedagogical example"