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There appears to be a newer and more extensive paper that encompasses and expands on Lentz' work, while also claiming Lentz's paper was mathematically incomplete or un-reproducible in some way: Bobrick A, Martire G. Introducing physical warp drives. Classical and Quantum Gravity. 2021 Jan 25. https://arxiv.org/abs/2102.06824 from the abstract: ...We present the first general model for subluminal positive-energy, spherically symmetric warp drives; construct superluminal warp- drive solutions which satisfy quantum inequalities; provide optimizations for the Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetime in which space capacity and the rate of time can be chosen in a controlled manner. Conceptually, we demonstrate that any warp drive, including the Alcubierre drive, is a shell of regular or exotic material moving inertially with a certain velocity. Therefore, any warp drive requires propulsion. We show that a class of subluminal, spherically symmetric warp drive spacetimes, at least in principle, can be constructed based on the physical principles known to humanity today. from pg. 3: ...(Natario 2002) constructed a warp drive solution without space contraction or expansion, contrary to the earlier assumption that it facilitated the movement of warp drives. (Natario 2006) constructed a new subluminal warp drive solution in the weak-field regime, which required negative energies. (Loup et al. 2001) had previously introduced a modified version of the Alcubierre drive intended to alter the rate of time for the observers inside the bubble. However, their modification reduces to the original Alcubierre metric, as we also show in Appendix A. Finally, (Lentz 2020) has recently proposed a warp drive metric claiming to have purely positive energy everywhere in both subluminal and superluminal regimes, although without providing means to reproduce the study. The works above, to our knowledge, summarize all the modifications of the Alcubierre drive available in the literature. Superluminal travel had also been studied by (Krasnikov 1998) and (Everett & Roman 1997). In these studies, the authors introduced Krasnikov tubes... --- edit- adding quote from pg 4 for context: In Section 4, we introduce a simple method to construct warp drive metrics by choosing the state of spacetime inside them. Additionally, we show that the Alcubierre metric is only a particular member of a much more general class of warp drive solutions admitting negative energy densities. Subsequently, we construct several spacetimes with a range of new properties. We introduce a macroscopic negative- energy drive which satisfies quantum inequalities, as well as several metrics with negative-energies which allow one to control the rate of time and spatial contraction inside the drive. In Section 5, we review the interpretation of warp drives in light of this study. |