In general relativity the vacuum speed of light is locally invariant, but not globally invariant. The vacuum speed of light remote from a given observer need not be c. It can be greater than c and can vary with direction depending on the gravitational field involved. Because this is allowed - starships that travel between the stars faster than c are not ruled out a-priori within the physics of general relativity.
I pinged an astrophysicist friend of mine who is more a gravitational physicist than I. and this is what he wrote back:
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I'm not an expert on GR but there are several things wrong with this reply.
1) Even if there is some effect of GR that causes a gravitational field to allow a "vacuum speed of light" (whatever that is) to vary with direction or be greater than c it would only occur where there are strong gravitational fields. Since the claim is about travel between stars this is not relevant.
2) I don't think that that the speed of light can vary in GR anymore than it can vary in SR. I also have no idea what he means by local vs global invariance.
3) The difference between SR and GR is the treatment on non-inertial reference frames via the principle of equivalence. I don't see how this allows a change to the basic assumption of SR, the invariance of the speed of light. I could be all wet here but I've never heard of this before.
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I have added a few web pages that may explain this a little better:
http://www.maths.soton.ac.uk/relativity/GRExplorer/Einstein/curved.htm
http://www.astronomynotes.com/relativity/s4.htm
The only thing I can think you are referring to is using exotic matter (with imaginary mass). I found a description of what I believe you are referring to:
http://home.sunrise.ch/schatzer/space-time.html
To Physicist: If I am all wet, feel free to shoot me down! :)