On Restrictions of Current Warp Drive Spacetimes and Immediate Possibilities of Improvement
Abstract
1. Brief Recap on the State-of-the-Art of Warp Drive Spacetimes
2. Covariant Spatial Motion
2.1. General Kinematics of Covariant Spatial Motion
2.2. Properties of Restricted Warp Drives
2.3. Properties of Tilted Warp Drives
2.4. Comparison of Restricted and Tilted Lagrangian Warp Drives
3. T-Warp: A New Concept Beyond Current Proposals
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
1 | |
2 | A bar under the symbol denotes the metric dual 1-form of a given vector field tangent to the given manifold. |
3 | By covariant Lorentz-factor we emphasize that it is a function of the covariant velocity . |
4 | |
5 | In the covariant setting, observers moving along the normal congruence are commonly named Eulerian observers. |
6 | In [5], Alcubierre compares the proper time of the spaceship with a “distant observer in the flat region”, i.e., an observer at rest at infinity since the Alcubierre metric is asymptotically flat. For such observer and , hence . Therefore, there is no time dilatation between the spaceship and the distant observer. However, there is time dilatation between the spaceship and an observer in the vicinity of the spaceship. More precisely, since the shift vector is assumed to rapidly tend to zero outside the ‘warp bubble’, the coordinate observer becomes an Eulerian observer and time dilatation vanishes. But, in other models where the shift vector decays more slowly there is more significant time dilation. |
7 | With some exceptions including the metric introduced by Van Den Broeck [22], where the author generalized the Alcubierre metric slightly by considering conformally flat slices. |
8 | The relation (16) might merely serve as an intuition as there is no need to define the spatial covariant velocity in this way because (4) is covariantly well-defined (see, e.g., [20] (Section 7.3)). The reader may consult [18] (Section 6.3.1), in particular Figures 6.1 and 6.2. (cf. Figure 1b below). We here think of the covariant spatial velocity that results in the infinitesimal displacement vector after the elapsed proper time differential (which are both not exact forms, although we use the same symbol by abuse of notation; this also applies to (14)). |
9 | We herewith also specify a relation between lapse and shift a priori. We believe, however, that this choice implies a number of advantages, at least serving as a first step to realize the T-Warp concept with sufficient generality. |
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Barzegar, H.; Buchert, T. On Restrictions of Current Warp Drive Spacetimes and Immediate Possibilities of Improvement. Universe 2025, 11, 293. https://doi.org/10.3390/universe11090293
Barzegar H, Buchert T. On Restrictions of Current Warp Drive Spacetimes and Immediate Possibilities of Improvement. Universe. 2025; 11(9):293. https://doi.org/10.3390/universe11090293
Chicago/Turabian StyleBarzegar, Hamed, and Thomas Buchert. 2025. "On Restrictions of Current Warp Drive Spacetimes and Immediate Possibilities of Improvement" Universe 11, no. 9: 293. https://doi.org/10.3390/universe11090293
APA StyleBarzegar, H., & Buchert, T. (2025). On Restrictions of Current Warp Drive Spacetimes and Immediate Possibilities of Improvement. Universe, 11(9), 293. https://doi.org/10.3390/universe11090293