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The warp drive: hyper-fast travel within general relativity
Open accessAbstract
It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the `warp drive' of science fiction. However, just as happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.
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In the citing paper
“In this situation explicit computation shows that the NEC, and so the SEC, WEC and DEC, are all explicitly violated.See specifically the original discussion in [1], and the subsequent follow-up discussions in [12][13][14][15][16][17], and [20,21].”
From ADM mass in warp drive spacetimes (2023) · cites this paper as [1]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“For the Alcubierre warp bubble the flow field v(t, x) is auto-parallel. That is v(t, x) = v(t, x) v;v = (constant).”
From ADM mass in warp drive spacetimes (2023) · cites this paper as [1]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The transport logistics of the presented positive-energy solitons are similar to the solitons of the Alcubierre solution.”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The solution of [1] possesses only one negative expansion lobe at the leading edge of its soliton and one positive expansion lobe at the trailing edge.”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The largest values of θ for the positive-energy soliton coincide with the sources of stress-energy density, in contrast to the solution of Ref. [1] where the energy density and expansion factor are maximally separated on the soliton boundary.”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
Experimental — accuracy not yet measured
The cited source says what the claim attributes to it.
In the citing paper
“Alcubierre warp drives have long been known to violate the WEC [9]”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [9]
The cited source says what the claim attributes to it.
In the citing paper
“This argument applies, in particular, to all three of the Alcubierre [9], Nat´ ario zeroexpansion [10], and Lentz/Fell-Heisenberg zero-vorticity [1, 3] warp drives, and also (for slightly different reasons) to the model warp drives considered by Bobrick-Martire [2].”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [9]
The cited source says what the claim attributes to it.
In the citing paper
“Specifically, in Alcubierre's original article [9, equation (6)] the concrete realization of the shape function f ( r s ) he chooses, see equation (A.8), uses tanh functions and so does not have compact support. In this terminology, Alcubierre sets r inner = 0 and r outer = ∞ , which is certainly not a truncation.”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [9]
The cited source says what the claim attributes to it.
In the citing paper
“Alcubierre's solution allows for acceleration using a time-varying v s ( t ).”
From Constant velocity physical warp drive solution (2024) · cites this paper as [1]
The cited source says what the claim attributes to it.
In the citing paper
“Alcubierre's solution is a shift vector addition to an otherwise Minkowski spacetime.”
From Constant velocity physical warp drive solution (2024) · cites this paper as [1]
The cited source says what the claim attributes to it.
In the citing paper
“Thus, it is clear that all the characteristic warp drive features of this spacetime are sourced purely by the shift vector.”
From Constant velocity physical warp drive solution (2024) · cites this paper as [1]
The cited source says what the claim attributes to it.
In the citing paper
“In a seminal paper, Alcubierre also concluded that the warp metric would imply the violation of the energy conditions since it appeared that a negative energy density would be required for the creation of the warp bubble.”
From Fluid dynamics in the warp drive spacetime geometry (2021) · cites this paper as [1]
The cited source says what the claim attributes to it.
In the citing paper
“The field equations of general relativity (GR) permit inertial observers to be transported at superluminal rates relative to distance observers.”
From Positive energy warp drive from hidden geometric structures (2021) · cites this paper as [6]
The cited source says what the claim attributes to it.
In the citing paper
“The multi-compartment structure is a distinct departure from the single top-hat soliton fond in [1] and [11].”
From Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory (2021) · cites this paper as [1]
In the citing paper
“The Einstein tensor components were calculated and it was noticed that negative energy density would be required to create the warp bubble, thus violating the weak and dominant energy conditions.”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
In the citing paper
“In the original paper by M. Alcubierre the warp drive metric was established without solving the Einstein equations [1].”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
In the citing paper
“The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a spacetime distortion, called warp bubble, to travel with superluminal global velocities.”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
In the citing paper
“Motivated by the fact that neither the original paper by Alcubierre, nor the subsequent ones cited above, did actually solve the Einstein equations using the warp drive metric, we proceed to investigate possible solutions for a dust particle energy momentum tensor [26].”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
In the citing paper
“In Ref. [1] the Einstein equations were not solved, since the metric was merely guessed with a form function (see Eq. 2.8) that rules the warp bubble shape.”
From Perfect fluid warp drive solutions with the cosmological constant (2021) · cites this paper as [1]
In the citing paper
“So far the proposed solutions have been unphysical, requiring energy condition violations and large energy requirements.”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
In the citing paper
“The first warp drive solutions developed by Alcubierre [1] and then further developed by Van Den Broeck [16] enabled passengers inside the warp bubble to move at arbitrary speeds but at the cost of both enormous energy density and unphysical stress-energy tensors using negative energy.”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
In the citing paper
“The Alcubierre metric violates all energy conditions within the bubble region, as it necessitates negative energy density, as Alcubierre demonstrated. This fact is confirmed through the analysis conducted using Warp Factory.”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
In the citing paper
“In line with the Star Trek conception of warp drives, the first warp solution from Alcubierre was constructed such that the passengers and external observers both experience the same passage of time (proper time).”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
In the citing paper
“For example, Alcubierre has a flat passenger volume and a warp bubble whose spatial extent is determined by a shape parameter 9 .”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
In the citing paper
“Alcubierre introduced the first general relativistic warp drive in 1994 [1].”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [1]
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Newtonian limits of warp drive spacetimes
Natário, J. (2006) · General Relativity and Gravitation · doi:10.1007/s10714-006-0234-0 · Cited by 9
“ction Newtonian limits of relativistic spacetimes are useful tools for understanding and interpreting these (see [Ehl91], [Ehl97] and references therein). The warp drive spacetime, first introduced in [Alc94], is an interesting example of a relativistic spacetime, sheding light on the nature and limits of General Relat…”
MethodA time machine for free fall into the past
Fermi, D., & Pizzocchero, L. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aace6e · Cited by 9
Macro-perspectives beyond the world system
Voros, J. (2024) · Swinburne figshare (Swinburne University of Technology) · doi:10.25916/sut.26244803 · Cited by 9
The Mystical Formula and The Mystery of Khronos
Orfeu Bertolami, A. (2009) · Springer eBooks · doi:10.1007/978-90-481-3475-5_11 · Cited by 10
How to produce exotic matter using classical fields
Vollick, D. N. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.56.4720 · Cited by 9
Engineering the Zero-Point Field and Polarizable Vacuum For Interstellar FlightPreprint
Puthoff, H. E., & Little, S. R. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1012.5264 · Cited by 9
Classical and semi-classical energy conditionsPreprint
Martín–Moruno, P., & Visser, M. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1702.05915 · Cited by 49
“Moreover, stress-energy tensors violating the NEC can support hypothetical configurations as wormholes [9] and warp drives [25] in the framework of general relativity(6), which may lead to pathological situations.”
Curvature Invariants for the Accelerating Natário Warp Drive
Mattingly, B., Kar, A., Gorban, M., Julius, W., Watson, C. K., Ali, M. D., Baas, A., Elmore, C., Lee, J. S., Shakerin, B., et al. (2020) · Particles · doi:10.3390/particles3030042 · Cited by 9
“Alcubierre used the York time, which is defined as Θ “ vs c x ́xs rs d f drs , to map the volume expansion of a warp drive [1].”
Detailed study of null and timelike geodesics in the Alcubierre warp spacetime
Müller, T., & Weiskopf, D. (2011) · General Relativity and Gravitation · doi:10.1007/s10714-011-1289-0 · Cited by 8
“The Warp metric developed by Miguel Alcubierre [2] can be described by the line element ds2 = −c2dt2 + [dx − v f (r)dt]2 + dy2 + dz2, (1) where c is the speed of light, v = dx(t)/dt , r(t) = √ (x − x(t))2 + y2 + z2, f (r) = tanh(σ (r + R))− tanh(σ (r − R)) 2 tanh(σ R) , (2) and x(t) is the worldline of the center of t…”
Cylindrically symmetric pure radiation space-time and closed timelike geodesics
Ahmed, F. (2017) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptx041 · Cited by 8
Concepts for Deep Space Travel: From Warp Drives and Hibernation to World Ships and Cryogenics
Braddock, M. (2018) · Current Trends in Biomedical Engineering & Biosciences · doi:10.19080/ctbeb.2018.12.555847 · Cited by 8
“[8-10] No space debris to collide with vessel Extremely high energies would be required”
BackgroundRelativistic rocket: Dream and reality
Semyonov, O. G. (2014) · Acta Astronautica · doi:10.1016/j.actaastro.2014.01.027 · Cited by 8
“Putting aside such sci-fi projects as "warp drive" [3,4], the prospects of jet propulsion for reaching the stars will be discussed below, where the term ‘jet’ is used in its general sense as a flow of material entities either massive or massless but carrying a mechanical momentum.”
BackgroundDiscontinuous quantum evolutions in the presence of closed timelike curves
DeJonghe, R., Frey, K., & Imbo, T. D. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.087501 · Cited by 8
White, H. G., Vera, J., Han, A., Bruccoleri, A. R., & MacArthur, J. V. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-09484-z · Cited by 8
Experimental Concepts for Generating Negative Energy in the Laboratory
Davis, E. W. (2006) · AIP conference proceedings · doi:10.1063/1.2169321 · Cited by 8
“Alcubierre’s discovery in 1994 of the “warp drive” spacetime metric, which was another solution to Einstein’s GTR field equations. Alcubierre (1994) derived a metric motivated by cosmological inflation that would allow arbitrarily short travel times between two distant points in space.”
BackgroundWhy gravity experiments are so exciting
Lämmerzahl, C. (2008) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2008-00823-7 · Cited by 8
Gravitational radiation and its application to space travel
Fontana, G. (2000) · AIP conference proceedings · doi:10.1063/1.1290910 · Cited by 8
The vacuum state of quantum gravity contains large virtual massesPreprint
Modanese, G. (2007) · Cited by 13
Warp Drive: A New ApproachPreprint
Obousy, R., & Cleaver, G. (2008) · Cited by 8
Расчёты для межзвёздных кораблей в гипотезе Acta UniversiPreprint
Ященко, Д. (2026) · doi:10.24108/preprints-3114202 · Cited by 8
ADM mass in warp drive spacetimes
Schuster, S., Santiago, J., & Visser, M. (2023) · General Relativity and Gravitation · doi:10.1007/s10714-022-03061-9 · Cited by 8
“See specifically the original discussion in [1], and the subsequent follow-up discussions in [12–17], and [20, 21].”
Undermining Motivations for Universalism
Effingham, N. (2011) · Noûs · doi:10.1111/j.1468-0068.2010.00779.x · Cited by 7
Making Stargates: The Physics of Traversable Absurdly Benign Wormholes
Woodward, J. F. (2011) · Physics Procedia · doi:10.1016/j.phpro.2011.08.003 · Cited by 7
“Similar densities, as a matter of idle interest, are required to make the “warp drives” proposed several years later by Alcubierre [2] Construction of devices that demand exotic matter of such densities seems, on its face, insuperable.”
Time travel paradoxes and multiple histories
Hauser, J., & Shoshany, B. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.064062 · Cited by 7
“Although these spacetimes were clearly unphysical – the wormholes were non-traversable and the cosmologies unrealistic – they were followed, several decades later, by traversable wormholes, warp drives, and other spacetimes supporting time travel [8, 9, 10, 11, 12, 13].”
Background
Metadata
- Authors
- Alcubierre, M.
- Affiliations
- University of Wales (GB)
- Corresponding author
- Alcubierre, Miguel
- ORCID
- Alcubierre, Miguel
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1994-05-01
- Volume
- 11
- Issue
- 5
- Pages
- L73-L77
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2118757814
- Semantic Scholar
- 0e1f6aaae0fc62e638e46804c418ad71d27b6533
- Cited by
- 569
- References
- 3
- Citations by year
- 2026: 25 · 2025: 41 · 2024: 30 · 2023: 24 · 2022: 30 · 2021: 22 · 2020: 42 · 2019: 18 · 2018: 12 · 2017: 24 · 2016: 16 · 2015: 8 · 2014: 8 · 2013: 22 · 2012: 21
- FWCI
- 8.84
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- warp drive, faster-than-light travel, general relativity, spacetime distortion, exotic matter, wormholes, superluminal motion
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