Curvature Invariants for the Accelerating Natário Warp Drive

Round 1

Reviewer 1 Report

In this paper the authors calculate the curvature invariants R, r_1, r_2 and w_2 in an accelerating Natário warp drive spacetime, and they are computed and plotted against several parameters: time, acceleration, skin depth and radius of the warp bubble. Finally, several features about the internal structure of the warp bubble are discussed. The results are presented in a clear and concise way through a set of plots in the appendix. The paper is scientifically sounding and deserves to be published. A minor comment that I would like to make is in Eq.(5). It would help for clarity if the authors make a more clear distinction between the numerical range on which every set of indices varies. For instance, that they could specify that i,j=0,..,3 and, on the other hand, \alpha=1,..,3. This confusion emerges immediately in the next equation (6), on which the new Cartesian coordinates (X,Y,Z) are labeled again by i, which now ranges from 1 to 3. And finally in Eq.(12) the null tetrad vectors are labeled again with the subindex i, which presumably goes from 0 to 3. Besides this, I don't see any other minor issue.

Author Response

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Reviewer 2 Report

I don't recommend publication in its current state. In my opinion, this article presents several structural problems.

First, throughout the article, it is never properly established what is the problem solved. It is not clear, for instance, if the invariants are difficult to compute and the authors are providing an approach? In this regard, it is not clear why r1, r2, and w2 are relevant for the study and not any other invariant. By the same token, did the numerical approach followed required a previously unknown insight? Are the graphics a new way to visualize a previously known problem? The phrase “While the individual functions are colossal in size and take a long time to calculate, their plots can be quickly scanned and understood.” would be very useful in this regard, along with a short explanation or discussion, if it were located at the introduction.

Second, the results are displayed in a not very illustrative fashion. Given the many graphics created, which are relegated to an appendix, it would have been illuminating to place them throughout the discussion. Instead, the authors provide just references to graphics. This is a little bit confusing and annoying.

Third, I am almost sure that not everyone is familiarized with the notation used. For instance, the r1, r2, and w2 invariants are constructed out of the \Psi’s and \Phi’s which are never defined in the paper. In my opinion, not any potential reader is familiarized with the physical meaning of the different the \Psi’s and \Phi’s.

I am confident the authors, after an extensive rewriting, can send a suitable-for-publication version of their work.

Author Response

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Reviewer 3 Report

This paper considers the utility of plotting curvature invariants for the accelerating Natario warp drive. By considering the well-known Carminati and McLenaghan invariants, which are scalar polynomial curvature invariants constructed from the Ricci and Weyl tensors, the authors have shown the benefit of plotting invariants to determine the physical properties of a spacetime.

I believe this paper has scientific merit, as it emphasizes the use of invariants as a tool to study spacetimes and potentially indicates the existence of crenelations in the invariants constructed from the Weyl tensor which could affect navigation. Of course the investigation of this problem should be complemented by an examination of the geodesic deviation equations, to fully understand what happens in the wake of the warp drive. However, given the computational demands of working with the accelerating Natario warp drive, this may not be practical (and may be another paper in itself), this lends credence to the argument that examining the invariants for a spacetime can give insight into a spacetime's properties in a straightforward manner. 

 

Author Response

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Round 2

Reviewer 2 Report

In my opinion, the new version of this work can be published in its current form. The authors made a genuine effort to make a much more readable manuscript. Maybe some phrases can be improved but the overall merit is not altered by this.