Historical research guide · 0301 · 2021
Generic warp drives violate the null energy condition
Jessica Santiago · Sebastian Schuster · Matt Visser
In one minute
Jessica Santiago, Sebastian Schuster and Matt Visser do the accounting for warp drives, and the result is the most useful constraint the field has. Working inside standard general relativity, they compute the whole stress-energy of a general warp field in Natário’s form — not only the energy density that one family of observers happens to see — and prove a clean theorem. If the null energy condition held everywhere, a quantity measuring how space is being stretched along a passing observer’s path could only ever decrease. But space has to come back to flat once the bubble has gone by, so that quantity must rise again. Something, somewhere in the shell, therefore sits below the ambient vacuum level, and every drive in the general family inherits it. This is not a closed door: it is a specification. The authors name the five places a warp programme can go next, and say plainly that one of them has to be faced.
Connection
Chapter 4 needs to know exactly what a warp shell costs, and this paper prices it: not ‘impossible’, but ‘here is the quantity you must supply, and here are the only places it can come from’. That is precisely the assignment chapter 2 takes up, because the vacuum — the one reservoir known to hold regions below its own ambient level — is where the site expects that supply to be found.
From the source
For a general warp field in Natário’s form, the energy density seen by the co-moving Eulerian observers is always a three-divergence plus a term that is negative semi-definite, the negative part being set by the vorticity of the shift flow.Section 4.1, Equations 4.3 to 4.6
The weak energy condition requires every timelike observer to see positive energy density, whereas the recent positive-energy warp proposals evaluate the density seen by one family — the co-moving Eulerian observers — so the two statements answer different questions.Section 1, introduction; Section 5, energy conditions
If the null energy condition holds, then along an Eulerian observer’s worldline the trace of the extrinsic curvature can never increase: its proper-time derivative is at most minus three halves of the trace of the squared trace-free extrinsic curvature, which is itself never positive.Section 7.4, Equation 7.34
Because the spacetime must return to its flat asymptotics after the bubble has passed, that trace has to rise again — so any warp drive in the general Natário form violates the null energy condition somewhere along those worldlines, and with the null condition violated the weak, strong and dominant conditions follow.Section 7.4, restoration of asymptotics; Section 8, conclusions
The proof needs only that the warp drive’s contribution to the extrinsic curvature is sufficiently localised: it assumes no zero ADM mass and uses no integration by parts, which is what makes it apply to the whole class rather than to one metric.Section 7.4, closing note on the proof
Five routes remain open and the authors list them for the field: modify the theory of gravity, modify the definition of a warp drive, modify the energy conditions, appeal to macroscopic quantum physics, or allow singularities or closed timelike curves — and in modified gravity the purely geometrical null and timelike convergence conditions still apply whenever the field equations can be rearranged as Einstein tensor equals an effective stress-energy tensor.Section 6, convergence conditions; Section 8, discussion and conclusions
The way in
https://arxiv.org/abs/2105.03079How to cite it
Jessica Santiago, Sebastian Schuster, Matt Visser (2021) Generic warp drives violate the null energy condition doi:10.1103/PhysRevD.105.064038