Closed Timelike Curves Re-Examined

Abstract

Examples are given of the creation of closed timelike curves by choices of coordinate identifications. Following G\"odel's prescription, it is seen that flat spacetime can produce closed timelike curves with structure similar to that of G\"odel. In this context, coordinate identifications rather than exotic gravitational effects of general relativity are shown to be the source of closed timelike curves. Removing the periodic time coordinate restriction, the modified G\"odel family of curves is expressed in a form that retains the timelike and spacelike character of the coordinates. With these coordinates, the nature of the timelike curves is clarified. A helicoidal surface unifies the families of timelike, spacelike and null curves. In all of these, it is seen that as in ordinary flat spacetime, periodicity in the spatial position does not naturally carry over into closure in time. Thus, the original source of serious scientific speculation regarding time machines is seen to be misconceived.