A potentially stable spacetime topology
that may permit time travel
Time travel has become a theoretical possibility. The concept depends on the existance of closed timelike curves (CTCs). One manifestation of this is a wormhole in four-dimensional Einstein gravity. The problem with a wormhole topology is that the inward pressure on the tunnel is so large, it implies the necessity of negative-energy densities and a pinching off of the wormhole.
A ringhole is a torus like topology where there is no violation of the weak energy condition in classical general relativity. When one ringhole mouth is kept at rest and the other moves with sufficiently high velocity, then it is concieveable that an advanced civilization could use this phenomenon to traverse time in a particular worldline. If the universe is indeed characterized by a quantum foam, then things such as ringholes may indeed be possible.
For more information, read:
The Large Scale Structure of Space-Time SH Hawking, GFR Ellis - 1973
Ringholes and closed timelike curves PF Gonzalez-Diaz, Physical Review D v54 p 6122 1996.