W. J. Van Stockum, (1910 - 1944) was an important early contributor to the development of general relativity. He was a Dutch mathematician. Stockum showed in 1937, a possible solution to Einstein's equations that would allow for time travel. This situation would make use of a concept in general relativity known as "frame-dragging." This is when a rotating mass can actually drag and distort surrounding spacetime. Stockum's idea involved a cylinder of infinite size (although not physically possible), spinning around at the speed of light, it would drag the spacetime around with it. The traveler, who moves across the cylinder will move at fantastic velocities. They would appear, to an outside observer, to be moving faster than the speed of light. If one made a complete trip around the cylinder, they would have returned before they left, hence, went back in time!
The faster the cylinder spun, the further back in time you would go. However, you could not go back farther than the creation of the cylinder itself. However, there are two phenomenon that make such a time machine impossible:
Cylinders cannot be infinitely long.
The cylinder, would move near the speed of light. Hence, the centrifugal forces would be so large, that the material that the cylinder is composed of would fly apart.
There is also the Tipler cylinder. This is an approach to time travel that requires a dense spinning cylinder. The cylinder would have to be infinitely long, and be spinning about its axis at a sufficient speed. A spacecraft flying around the cylinder in a circular path could move backwards or forwards in time. However, ordinary matter, sadly is not strong enough to construct such a device.