Generic warp drives violate the null energy condition
Jessica Santiago · Sebastian Schuster · Matt Visser
Abstract and summary · read the original at the source
In one page
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.
Why it matters hereChapter 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.
What it claims
01For 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
Published and peer-reviewed02The 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
Published and peer-reviewed03If 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
Published and peer-reviewed04Because 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
Published and peer-reviewed05The 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
Published and peer-reviewed06Five 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
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Read it · abstract
Abstract
Three very recent articles have claimed that it is possible to, at least in theory, either set up positive energy warp drives satisfying the weak energy condition (WEC), or at the very least, to minimize the WEC violations. These claims are at best incomplete, since the arguments presented only demonstrate the existence of one set of timelike observers, the co-moving Eulerian observers, who see "nice" physics. While these observers might see a positive energy density, the WEC requires all timelike observers to see positive energy density. Therefore, one should revisit this issue. A more careful analysis shows that the situation is actually much grimmer than advertised -- all physically reasonable warp drives will violate the null energy condition, and so also automatically violate the WEC, and both the strong and dominant energy conditions. While warp drives are certainly interesting examples of speculative physics, the violation of the energy conditions, at least within the framework of standard general relativity, is unavoidable. Even in modified gravity, physically reasonable warp drives will still violate the purely geometrical null convergence condition and the timelike convergence condition which, in turn, will place very strong constraints on any modified-gravity warp drive.
The way in
https://arxiv.org/abs/2105.03079Posted to arXiv under the arXiv.org perpetual non-exclusive licence, so this page carries the summary, the claims and the authors’ own abstract, and sends the reader to the source. Published as Physical Review D 105, 064038 (2022).
How to cite it
Jessica Santiago, Sebastian Schuster, Matt Visser (2021) Generic warp drives violate the null energy condition. doi:10.1103/PhysRevD.105.064038
Where it sits in the curriculum
The metric, warp drives and wormholesWhat the vacuum isThe evidence ladder