Warp drive causality issue, and a possible error in a paper?
Take a look at this paper on "Warp Drives and Causality:" https://journals.aps.org/prd/abstract/10.1103/PhysRevD.53.7365
The author attempts to argue that the Alcubierre Drive spacetime could exhibit Closed Timelike Curves, if one is to consider a "Lorentz Transformation of the coordinates." In such coordinates, one finds that a light ray emitted on board the ship could travel backwards in time in such coordinates.
The author seems to confuse unphysical coordinate artifact with actual phenomenology. As far as I understand, in GR, one has the freedom to label points on the spacetime manifold by whatever $t, x, y, z$ they like, but the metric tensor remains a physical invariant, regardless of what you call your coordinates. However, its representation in a coordinate system will of course depend on your choice of coordinates.
To be mathematically precise, one cannot perform a Lorentz Transformation on the coordinates within the context of a curved spacetime as in GR. 275
If we want to of course, we could transform <PERSON> coordinates, to coordinates which look like a Lorentz Boost, but then we must transform the representation of the metric as well, and in our case we don't have the Minkwoskian structure as we do in SR.
A light beam propagating inside the vessel will remain within its local light cone, regardless of what you call your coordinates, as specified in <PERSON>'s original paper. The "Lorentz transformation" attempted by the author does not hold.
Generally speaking, to find a CTC, we are looking for a Timelike trajectory for a particle in the spacetime that returns to the same point on the spacetime manifold. In summary, I do not see that a CTC arises, but that the paper concludes the existence of CTC from a violation of causality in special relativity which is exactly what a CTC does not entail AND an attempt to apply special relativity beyond its domain of applicability. Lorentz Boosts could only be defined Locally at a point in GR, and not the entire spacetime.
I am only a student, and the author is surely more experienced in GR than me, but I can't see where I am wrong: could someone kindly explain to me where my attempted refutation fails? Sorry for the excessive text... 275