Semiclassical instability of dynamical warp drives
Stefano Finazzi · Stefano Liberati · Carlos Barceló
Abstract and summary · read the original at the source
In one page
Alcubierre’s warp drive carries a bubble of ordinary flat space across the universe faster than light while nothing inside it moves quickly at all. Stefano Finazzi, Stefano Liberati and Carlos Barceló ask what the quantum vacuum does once you switch it back on. Earlier work had only treated a bubble that had always existed; these three build one instead, starting from flat space at rest and accelerating it to superluminal speed in a finite time, then computing the vacuum’s response — the renormalised stress-energy tensor — in a one-dimensional model simple enough to solve exactly. Two results follow. The bubble walls behave like horizons, so an observer riding inside is bathed in Hawking radiation whose temperature rises as the wall gets thinner. And on the front wall, which acts as a white-hole horizon, the vacuum energy grows exponentially on a timescale set by the wall thickness divided by the speed of light. A dynamically created superluminal bubble is therefore semiclassically unstable. A subluminal one is untouched.
Why it matters hereThis is the calculation chapter 4 has to know by name: it turns the question of whether quantum effects disturb a warp drive into numbers, and it identifies the design variable — the wall thickness sets both the temperature inside the bubble and how long the superluminal phase survives. It also marks where the work went next: subluminal bubbles are unaffected, and Barceló’s own 2022 follow-up in two and three spatial dimensions finds the divergence confined to isolated points carrying a finite amount of energy.
What it claims
01For an observer inside a superluminal warp-drive bubble the rear wall behaves as the horizon of a black hole and the front wall as the horizon of a white hole, and the paper works out that causal structure for both an eternal bubble and one created dynamically out of flat spacetime.Section I, Introduction; Section II, Causal structure of a superluminal warp drive
Published and peer-reviewed02An observer at the centre of the bubble generically sees a thermal flux of Hawking particles at the temperature set by the surface gravity of the rear horizon, and that surface gravity goes inversely with the thickness of the bubble wall — around a hundredth of the Planck temperature for the Planck-scale walls the quantum inequalities would impose, and about 0.003 kelvin for a wall one metre thick.Abstract; Section V, Summary and discussion, first and fifth paragraphs
Published and peer-reviewed03The renormalised stress-energy tensor grows exponentially with time on and near the front wall, so semiclassical backreaction becomes strong after a time of order the inverse surface gravity, roughly the wall thickness divided by the speed of light; a wall about 300,000 kilometres thick would be needed to stretch that growth time to a single second.Section IV, Eq. (83) and following; Section V, second and third paragraphs
Published and peer-reviewed04Hawking radiation produced at the rear horizon also accumulates without bound on the Cauchy horizon of the dynamical geometry, the energy density growing as the exponential of twice the surface gravity times time through the blueshift factor — an effect of the same family as the long-studied instability of inner horizons in Kerr-Newman black holes, and one that does not arise if the superluminal phase is held for only a finite time.Section IV, Eqs. (85) to (87); Section V, fourth paragraph
Published and peer-reviewed05A bubble that stays subluminal forms no horizons, creates no Hawking radiation and shows neither the high temperature nor the white-horizon instability; the exotic matter needed to hold the geometry together is the only requirement that remains.Section V, closing paragraph
Published and peer-reviewed06The calculation is carried out in one space and one time dimension, the only case that can be treated fully analytically, and the authors expect rather than demonstrate that the features survive a full three-dimensional treatment; they also flag that the divergence on the front wall may disappear if Lorentz symmetry is broken at high energies, and name analogue-gravity systems as the place where that could be settled experimentally.Section V, sixth and seventh paragraphs
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Abstract
Warp drives are very interesting configurations in general relativity: At least theoretically, they provide a way to travel at superluminal speeds, albeit at the cost of requiring exotic matter to exist as solutions of Einstein’s equations. However, even if one succeeded in providing the necessary exotic matter to build them, it would still be necessary to check whether they would survive to the switching on of quantum effects. Semiclassical corrections to warp-drive geometries have been analyzed only for eternal warp-drive bubbles traveling at fixed superluminal speeds. Here, we investigate the more realistic case in which a superluminal warp drive is created out of an initially flat spacetime. First of all we analyze the causal structure of eternal and dynamical warp-drive spacetimes. Then we pass to the analysis of the renormalized stress-energy tensor (RSET) of a quantum field in these geometries. While the behavior of the RSET in these geometries has close similarities to that in the geometries associated with gravitational collapse, it shows dramatic differences too. On one side, an observer located at the center of a superluminal warp-drive bubble would generically experience a thermal flux of Hawking particles. On the other side, such Hawking flux will be generically extremely high if the exotic matter supporting the warp drive has its origin in a quantum field satisfying some form of quantum inequalities. Most of all, we find that the RSET will exponentially grow in time close to, and on, the front wall of the superluminal bubble. Consequently, one is led to conclude that the warp-drive geometries are unstable against semiclassical backreaction.
Stefano Finazzi and Stefano Liberati (SISSA and INFN Trieste), Carlos Barceló (Instituto de Astrofísica de Andalucía, CSIC, Granada). Physical Review D 79, 124017 (2009). Author version: arXiv:0904.0141, revised 14 July 2009.
(Abstract only. The author version is free to read at https://arxiv.org/abs/0904.0141 and the published article at https://doi.org/10.1103/PhysRevD.79.124017 — see the rights note for why the full text is not reproduced here.)
The way in
https://doi.org/10.1103/PhysRevD.79.124017Licence checked directly. The published article carries the APS default license, and the author version posted as arXiv:0904.0141v2 (14 July 2009) is under arXiv’s non-exclusive distribution licence — neither carries a Creative Commons statement. Only the abstract is reproduced here; the author version is free to read on arXiv. The summary and claims below were written from the complete text of that version.
How to cite it
Stefano Finazzi, Stefano Liberati, Carlos Barceló (2009) Semiclassical instability of dynamical warp drives. doi:10.1103/PhysRevD.79.124017
Where it sits in the curriculum
The metric, warp drives and wormholesThe vacuum as a quantum fluid