PHYSICAL AND STABLE CLOSED TIME-LIKE CURVES

Abstract

We construct a class of closed time-like curves (CTCs) using a compactified extra dimension u. A nonzero metric element gtu(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.