Every point in space-time has its own light cone. Accepting that space-time can be curved by heavy gravity, as predicted by general relativity, it is possible to tilt light cones. With enough space-time curvature, a particle could keep moving into its own local future at less-than-light speeds while also traveling along a world line that "loops" back on itself.

Based upon the reletavitistic approach to rotating matter, by creating a "sufficiently large rotating cylinder," we can create a distortion in space-time that causes light cones to tilt. Of couse this cylinder must be made of a huge piece of material approximately ten time the mass of the sun. It must also be forced to rotate at a few million revolutions per minute. Once the cylinder is constructed, by travelling in a carfully plotted course around the cylinder, a particle could travel into the past and back again to the original point of departure. Below is a conceptual drawing of the cylinder as proposed by the Time Travel Research Center.

Although a cylinder of this type is highly improbable to build, the important result is that the model does not violate any laws of physics or mathematics.