Hyperfast travel in general relativity

The problem is discussed of whether a traveler can reach a remote object and return sooner than a photon would when taking into account that the traveler can partly control the geometry of his world. It is argued that under some reasonable assumptions in globally hyperbolic space-times the traveler cannot hasten reaching the destination. Nevertheless, it is perhaps possible for the traveler to make an arbitrarily long round-trip within an arbitrarily short (from the point of view of a terrestrial observer) time.