We show that, although a single Krasnikov tube does not involve closed timelike curves, a time machine can be constructed with a system of two nonoverlapping tubes. Inside the tube spacetime is flat, but the light cones are opened out so as to allow superluminal travel in one direction.

In our four-dimensional extension of this metric, a 'tube' is constructed along the path of an outbound spaceship, which connects the Earth and the star. As a consequence, the Krasnikov metric has the interesting property that, although the time for a one-way trip to a distant star cannot be shortened, the time for a round trip, as measured by clocks on Earth, can be made arbitrarily short. We analyze and generalize a metric, originally proposed by Krasnikov for two spacetime dimensions, which does not suffer from the first difficulty.

One might hope that elimination of the first problem might ameliorate the second as well. In addition, such a bubble requires negative energy densities. Hence such an observer can neither create a warp bubble on demand nor control one once it has been created. The 'warp drive' metric recently presented by Alcubierre has the problem that an observer at the center of the warp bubble is causally separated from the outer edge of the bubble wall.

Warp drive