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In 1974, scientist
Frank Tipler published an
article, "Rotating Cylinders and the Possibility of Global Causality Violation", in a reputable
scientific journal, which used the theories of
general relativity in a rather unique way. The article described what could be considered a "
time machine" - and one that violates no known principles of
physics. It used no
wormholes, no
black holes, no
singularities.
A Tipler Cylinder is a long, (infinite, or nearly so) thin, super dense (neutron star-type material) cylinder, perhaps using about 10 times the mass of the sun. The cylinder would be spun around its axis at a speed of around a few billion revolutions per minute - at least half of the speed of light. This immense speed would be necssary to balance out the gravitational force exerted by the material, as it would be dense enough that it would otherwise collapse upon itself.
The key is that space-time is distorted by matter - the more matter in one place, the stronger the distortion. The extent of the distortion produced by this cylinder would allow something traveling at sub-light speeds to travel through time. Careful plotting of a spiral course around the cylinder will allow the time distortions to be utilized.
More detailed explanations depend on the concept of the "light-cone". A light-cone is a diagram of space-time, which represents the spatial dimensions, time, and the speed of light. They divide space-time into three areas - the past, the future, and a "forbidden" zone, delineated by the speed of light. The distortion of space-time caused by the cylinder would "tip" the light cones, eventually reaching a point where the portion representing the future would tip into the past. So as normal time progresses, it moves into the past, instead of the future, as they're overlapping.
There are some people who still believe there must be an error in the calculations somewhere, that this cannot be possible. To date, such an error has not been found. Another argument goes toward the cylinder's length - the original calculations were done with an infinite length cylinder, to simplify the calculations, but they would likely still apply to one of finite length - however, the concern is if such a finite length cylinder would collapse upon itself lengthwise due to gravity. Also, even if it is possible, then it would be limited in use - you would not be able to travel further into the past than the age of the cylinder.