zealo wrote:theory is that objects with a velocity higher than c have a negative time component right?
Imaginary, actually, so perhaps not too helpful. (The time dilation factor is the square root of 1-(v/c)^2, so the square root of a negative number if v>c.)
Also, there aren't solutions to GR that allow anything to accelerate through c in its local frame, which means that even if ftl travel was also time travel, that way of doing it wouldn't be possible in a system consistent with GR.
I have heard of two specific solutions. One is if the entire universe were rotating. I believe this is the GÃ¶del metric. The other involves rotating cosmic strings (i.e. long, stringy black holes
) around each other, creating closed timelike curves in the vicinity of where they pass.
These are obviously not really practical solutions, especially the one where the whole universe has to rotate. I think there are others that are more feasible (in that they only need a few galaxies' mass of negative energy to work, instead of the whole universe, for instance), but I don't know what they are.