Historical research guide · 0741 · 2024
On the Wormhole–Warp Drive Correspondence
Remo Garattini · Kirill Zatrimaylov
In one minute
Warp drives and wormholes are usually studied as two separate routes to the same destination. Remo Garattini and Kirill Zatrimaylov of the University of Bergamo ask what happens when you put one inside the other. Ellis had already shown that a black hole, written in the right coordinates, is literally a warp-drive metric — so a warp bubble can be embedded in a black hole exterior. Garattini and Zatrimaylov extend that to the Morris-Thorne wormhole, and find a genuine correspondence, though the warp metric it produces has curved spatial slices, which the standard Natario-Alcubierre definition does not allow. Then comes the twist. The conditions that make a wormhole safe for a human traveller — a throat that flares out, and no horizon — are exactly the conditions that make the throat a real curvature singularity as far as the warp bubble is concerned. So a warp drive can cross a wormhole that has a horizon, but not one a person could walk through. The authors name three ways the result might yet be evaded.
Connection
Chapter 4 keeps warp geometries and wormhole geometries in the same drawer because they are solutions of the same field equations, and this paper is the sharpest statement of how they actually fit together: not two vehicles, but one metric written two ways, with a specific obstruction where they meet. Chapter 2 supplies the shared cost, since both constructions call for energy densities below the ambient vacuum level. Read it beside Edward Teo’s rotating traversable wormholes at /library/stm-a473e80f36, Peter Kuhfittig on how little exotic material a traversable throat really needs at /library/stm-d54d953175, Sergey Sushkov’s phantom-energy wormholes at /library/stm-35489e8f11, and Alcubierre’s original warp metric at /library/stm-fc5383ec73.
From the source
Both constructions carry the same bill: a warp drive as Alcubierre defined it, and a Morris-Thorne wormhole, each require energy densities below the ambient vacuum level in order to exist at all.Section 1, Introduction
Ellis had already shown that the Schwarzschild metric written in Painlevé-Gullstrand coordinates is exactly a Natario-type warp metric, with the shift function equal to the square root of 2GM over r — which is what makes it possible to embed an actual warp drive in a black hole exterior by interpolating that shift against the bubble’s own velocity.Section 1; Eqs. 2.6 to 2.9
The same move generalises to the Morris-Thorne wormhole: a coordinate transformation brings the wormhole line element to warp form, with shift function the square root of one minus e to the 2Φ, but multiplied by a form factor equal to e to the Φ divided by the square root of one minus b over r — so the spatial slices are not flat and the Natario-Alcubierre definition of a warp drive has to be generalised to admit nonzero intrinsic curvature.Section 2, Eqs. 2.10 to 2.23
Taking the flare-out condition together with the throat condition and the no-horizon condition makes that form factor diverge at the throat, and computing the Ricci scalar shows the coefficients of the divergent terms cannot all be set to zero for any nonzero bubble shape function — so for the warp drive the throat is a genuine curvature singularity, not merely a coordinate one.Section 2, Eqs. 2.24 to 2.35
Interpolating the intrinsic metric as well makes the geometry inside the bubble locally Alcubierre, but the singularity is still felt by the shell — the region where the shape function lies strictly between zero and one — which is precisely where the throat passes through the bubble wall.Section 2, Eqs. 2.36 to 2.39; Figure 1
The paradoxical conclusion is that a wormhole with a horizon is not felt inside the warp bubble and can be traversed, while a humanly traversable wormhole cannot — and the authors name three loopholes that would settle it: the generalised proper-length transformation, whose free parameters may acquire physical meaning through the stress-energy tensor; the surgery construction that glues the two ends at a cutoff radius above the throat; and the fact that a singularity need not make the spacetime geodesically incomplete.Section 2, after Eq. 2.45; Section 3, Conclusions
The way in
https://arxiv.org/abs/2401.15136How to cite it
Remo Garattini, Kirill Zatrimaylov (2024) On the Wormhole–Warp Drive Correspondence arXiv:2401.15136