Does this preprint prove that warp drives are impossible? J. Santiago, S. Schuster and M. Visser, "Generic warp drives violate the null energy condition"
It states that the NEC (Null Energy Condition) is violated in this paper and many others: E. W. Lentz, "Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory"
It proves that warp drives violate an energy condition that many physicists think is reasonable. The universe of course has no obligation to be reasonable.
The NEC states roughly that the energy embodied in tension or negative pressure cannot be larger than the density of mass-energy somewhere. That is very extreme: no known material can do it, and were such things possible many other crazy things would be possible. Yet the energy conditions have not always worked so well. But few physicists would bet they can exist for real.
As Santiago et al say, there have been no-go theorems ruling out warp drives for decades. In fact, as far as I can tell, those earlier results already disprove the claims in Lentz and the other recent articles that Santiago et al are primarily responding to.
This doesn't mean that warp drives are impossible, as you can evade no-go theorems by violating their assumptions, but I think that no one, including Lentz, has managed to do that.
Earlier no-go results usually show violation of the weak (or sometimes strong) energy condition. Santiago et al show violation of the null energy condition, which is a stronger result. On the other hand they consider only warp drive geometries that can be written in a certain form. It is (they claim) general enough to include all or almost all of the warp drives proposed in the literature, but it seems less general that the definition of warp drive used in some previous no-go results.
No.
Regarding to that specific paper, they analysed only a family of metrics, which apparently does not even cover Lentz ansatz.
In general, be aware of no-go theorems that rely on too many assumptions. Even if you can argue with certainty that in the given mathematical framework something is impossible, you cannot guarantee that such framework, including every single assumption, describe our universe exactly.
No, it does not prove. Several authors have shown possible ways for the warp drive not to violate the energy conditions in specific cases [1,2,3]. Santiago et al. assumed those authors claimed the energy conditions are always respected but merely asserted are not always violated. These results [1,2,3] are counter-proof to theorems that assume generic warp drives always violate energy conditions, which does not invalidate the contributions of authors who tried to prove such theorems. Much of this discussion comes from Alcubierre's (1994) claim [4] that for his warp drive metric $$ ds^2 = - d t^2 + (d x + \beta d t)^2 + d y^2 + d z^2\,, $$ for the Eulerian observers with 4-velocities given by $$ u_\mu = (-1,0,0,0) \ \ , \ \ u^\mu = (1,-\beta,0,0) \,, $$ the energy density, as measured by those observers, can be obtained as $$ G^{\mu\nu} u_\mu u_\nu = -\frac{1}{4} \left[\left( \frac{\partial \beta}{\partial y} \right)^2 + \left( \frac{\partial \beta}{\partial z} \right)^2 \right] \leq 0\, \label{negeng} $$ and the above expression equals $G^{00}$, so Alcubierre concluded considering Einstein equations $G^{\mu\nu} = T^{\mu\nu}$ that the term $T^{00}$ regarded as the energy density for the energy-momentum tensor is always negative, and that the warp drive always violates the weak (WEC) and dominant (DEC) energy conditions. Alcubierre's claim is not wrong. However, he did not account for vacuum and complex solutions for Einstein's equations. If the shift vector is found to be of complex value, it is possible that the complex part will be negative and the real part will be positive. So, the WEC and DEC are not always violated. The validity conditions for theorems that state that any warp drive class always violates the energy conditions must be reviewed.
PS: The energy conditions are not general theorems. They are axioms used by Hawking and others to prove the "no-hair theorem for black holes". Several experimental pieces of evidence violate those conditions, i.e., cosmic inflation, negative energy density in cavities (Casimir effect), dark energy, etc.
References
[1] https://arxiv.org/abs/2102.06824
[2] https://arxiv.org/abs/2006.07125
[3] https://arxiv.org/abs/2104.06488
[4] https://arxiv.org/abs/gr-qc/0009013
[5] https://link.springer.com/article/10.1140/epjc/s10052-021-09484-z
