Physical and Stable Closed Timelike Curves
  We construct a class of closed timelike curves (CTCs) using a compactified extra dimension $u$. A nonzero metric element $g_{tu}(u)$ enables particles to travel backwards in global time $t$. The compactified dimension guarantees that the geodesic curve closes in $u$. The effective 2D ($t$ and $u$) nature of the metric ensures that spacetime is flat, therein satisfying all the classical stability conditions as expressed by the energy conditions. Finally, stationarity of the metric guarantees that a particle's energy is conserved. The pathologies that plague many hypothesized metrics admitting CTCs, e.g. an infinite cylinder of matter, a negative energy-distribution, particle acceleration/blue-shifting along the CTC, do not occur within our metric class. 
Chiu Man Ho and Thomas J. Weiler
gr-qc