Frankly speaking, I don't really understand this theory, but I can give a brief answer based on wikipedia:

"The Krasnikov Tube is a speculative mechanism for space travel involving the permanent warping of spacetime into superluminal tunnels."

"Serguei Krasnikov is a theoretical physicist at the Central Astronomical Observatory at Pulkovo in St. Petersburg, Russia. He identified what he saw as a critical flaw in Miguel Alcubierre's space warp proposal for space travel: if the space warp moves faster than the velocity of light, it cannot be controlled from inside. Krasnikov's analysis shows that at superluminal speeds the interior of the bubble is causally isolated from its surface and exterior. Photons cannot pass from the inside to the outside. Therefore, there would be no way of controlling the space warp—of stopping, starting or steering.

These problems might be circumvented by entering and exiting an Alcubierre space warp while it was travelling slowly, arranging for some automatic mechanism to raise the bubble velocity above the speed of light for a programmed period, and then lower the speed again in order to exit. This scheme is unworkable because material objects (like control computers and warp generators) in the skin of the bubble would be destroyed by the enormous forces generated from space annihilation or creation, while outside the bubble they would not travel at the superluminal speed of the interior and would be left behind.

Krasnikov's alternative is to create a space warp behind the space ship as it travels at near lightspeed to some distant star system, and then use the "tube" thus created for the return trip. This distortion of space has an interesting property for the return trip: it gets you back home shortly after you left, no matter how far you go.

In effect the Krasnikov tube is a tunnel through time, connecting the departure time of the ship with the time of its arrival. Inside the tube space-time is flat, but the path limits of light through space-time have been opened out so that it permits superluminal travel in one direction only; for example, back to the starting point on Earth."
Source(s):
http://en.wikipedia.org/wiki/Krasnikov_tube

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