Ringholes and closed timelike curves

It is shown that in a classical spacetime with multiply connected space slices having the topology of a torus, closed timelikes curves are also formed. We call these spacetimes ringholes. Two regions on the torus surface can be distinguished which are separated by angular horizons. On one of such regions (which surrounds the maximum circumference of the torus) everything happens like in spherical wormholes, but the other region (the rest of the torus surface), while still possessing a chronology horizon and nonchronal region, behaves like a converging, rather than diverging, lens and corresponds to an energy density which is always positive for large speeds at or near the throat. It is speculated that a ringhole could be converted into a time machine to perform time travel by an observer who would never encounter any matter that violates the classical averaged weak energy condition. Based on a calculation of vacuum fluctuations, it is also seen that the angular horizons can prevent the emergence of quantum instabilities near the throat.