Many Mathematicians and physicists have made models that appear to 'make sense' and seem to hint that time travel may be possible, Frank Tipler is one of these. His design relies on the frame dragging of light cones around massive, rotating objects, specifically cylinders.

The light cone or event cone as it is sometimes known is what really gives the structure to our universe and stops everything happening at once. It is what allows us to determine a causal chain of events, and Tipler realised that extreme manipulation of light cones could allow acausal things to occur, in other words a chain of events that would need a time machine to explain them.

In regions of rotating, high gravity objects, the space in which the light cone is embedded, swirls like a whirlpool. In the same way a yacht would be tipped over by the dragging of the water, so a light cone is tipped over by the dragging of space into the direction of the rotation. If you've drawn your light cones so that their sides have a 45-degree angle, a crucial point comes when the amount of tipping reaches 45o.
Consider two events separated in space, but at the same point in time; in low gravity field areas, nothing at event A can influence the event B. Moving in toward the high gravity area around a rapidly rotating, massive object, the light cones gradually tip over, when 45o is reached, the future part of the light cone of A touches the past light cone of B. At this point a ray of light emitted from event A can travel through the past light cone of B and influence this event, even though they are actually occurring at the same time! If you increase the tipping angle, things slower than the speed of light can influence event B, which is to say a spaceship could be flown through the light cones.

To an observer in flat space-time looking in towards this high gravity whirlpool of space it would look like the orbiting spaceship was travelling faster than the speed of light. To observers in the spaceship however it seems they are only moving at their normal speed.

Frank Tipler used this concept of light cone tipping to design a time machine. His design is, take a cylinder of material, ten times the mass of the sun, and rotate it up to several billion times per second. If you then orbit close to the cylinder, with the direction of the rotation, you can travel forwards in time, and against the rotation, backwards in time.
There are several problems with this design however, firstly you need to stop the ends of the cylinder collapsing in towards each other and forming a conventional black hole. (Perhaps threading the object with matter that has a negative energy density could stop this collapse.) Secondly for the maths to make sense, apparently the cylinder should be infinitely long. And thirdly you can only ever travel backwards or forwards in time to the point of the time machines creation or destruction.