Great question! Anyone who could answer that question would probably publish these results in some high-impact, prestigious, indexed journal.

In Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory, Lentz's idea is very creative and sophisticated, but it is still an idea and not a definite model for a warp drive. One has to define a metric with warp drive properties. Couple an energy-momentum tensor and solve Einstein equations, finding a KdV-type equation in terms of the shift vector governing the dynamics of the warp bubble, then defining the boundary and initial conditions from energy conditions, the null divergence of the energy-momentum tensor, and other properties imposing energy and matter density to be positive. This spacetime cannot allow closed timelike curves.

Jose Natario in Warp Drive With Zero Expansion demonstrated that warp drives with Cauchy surfaces in foliated spacetime will eventually violate Weak energy conditions because of no expansion volume, and a non-zero expansion will violate strong energy conditions. This is why in an Alcubierre drive, Eulerian observers will always perceive a warp bubble with non-positive energy density.

Also, in Warp Drive Basics, Alcubierre and Lobo demonstrated that there is an event horizon inside the warp bubble. So, the warp bubble may behave as a black (or white!) hole.

So, there is a very thin margin for constructing a physical warp drive with no pathologies. There are a lot of caveats.

Great question! Anyone who could answer that question would probably publish these results in some high-impact, prestigious, indexed journal.

In Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory, Lentz's idea is very creative and sophisticated, but it is still an idea and not a definite model for a warp drive. One has to define a metric with warp drive properties. Couple an energy-momentum tensor and solve Einstein equations, finding a KdV-type equation in terms of the shift vector governing the dynamics of the warp bubble, then defining the boundary and initial conditions from energy conditions, the null divergence of the energy-momentum tensor, and other properties imposing energy and matter density to be positive. This spacetime cannot allow closed timelike curves.

Jose Natario in Warp Drive With Zero Expansion demonstrated that warp drive with flat Cauchy surfaces will eventually violate Weak energy conditions because of no expansion volume, and a non-zero expansion will violate strong energy conditions. This is why in an Alcubierre drive, Eulerian observers will always perceive a warp bubble with non-positive energy density.

Also, in Warp Drive Basics, Alcubierre and Lobo demonstrated that there is an event horizon inside the warp bubble. So, the warp bubble may behave as a black (or white!) hole.

So, there is a very thin margin for constructing a physical warp drive with no pathologies. There are a lot of caveats.