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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 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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About apparent superluminal drives in generic gravity theories
Morales, J. O., & Santillán, O. P. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10323-y · Cited by 1
Huang, Z.-X. (2022) · Current Journal of Applied Science and Technology · doi:10.9734/cjast/2022/v41i1631726 · Cited by 1
Александров, В. А. (2022) · Письма в журнал технической физики · doi:10.21883/tpl.2022.14.55119.18899 · Cited by 1
Joseph, S. K. (2023) · International Journal of Modern Physics D · doi:10.1142/s0218271823500517 · Cited by 1
The warp drive and antigravityPreprint
Ellis, H. G. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0411096 · Cited by 1
“In a letter that appeared in 1994 in the journal Classical and Quantum Gravity Alcubierre exhibited a space-time metric that describes a surprising phenomenon occurring in a flat, euclidean space: a spherical region of the space glides along geodesically with a prescribed velocity vs(t) as if it were a (practically) r…”
Can a computer be "pushed" to perform faster-than-light?Preprint
Putz, V., & Svozil, K. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1003.1238 · Cited by 1
“Note that, although the speed of light barrier appears to be a fundamental limit for the transfer of “freely willable” information [40], several ways for “signals” trespassing the relativistic light cone [2], even to the extent of time travel [23, 33, 58, 12, 25], have been proposed.”
Superluminal Transformations in Spacetimes of Definite Metric
Peacock, K. A. (1998) · Springer eBooks · doi:10.1007/978-94-017-0990-3_27 · Cited by 1
“However, it might not apply to hypothetical ‘space warp’ methods of travel [1], since conceivably a locally Euclidean spatial metric could be maintained on board the starship.”
Analogue gravitational phenomena in Bose-Einstein condensatesPreprint
Finazzi, S. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1208.4729 · Cited by 2
“First, they are the acoustic analogues of interesting spacetimes in GR, such as Alcubierre’s warp drives [1] or Corley and Jacobson’s black hole lasers [47].”
InfluentialWormhole-Stargates: Tunneling Through The Cosmic Neighborhood
Davis, E. W. (2001) · Cited by 1
Space testing of electromagnetically sensitive materials for breakthrough propulsion physics
Holt, A. C., Davis, E. W., & Puthoff, H. (1999) · AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit · doi:10.2514/6.1999-2143 · Cited by 1
“the travelers would not return to Earth to find no one they knew left alive.(15)”
BackgroundCassenti, B. N., & Ringermacher, H. I. (2003) · AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit · doi:10.2514/6.2003-4677 · Cited by 1
Sonic Electromagnetic Gravitational Spacecraft
Sandu, C., & Brasoveanu, D. (2007) · AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (JPC) · doi:10.2514/6.2007-5119 · Cited by 1
Absolute quantum energy inequalitiesPreprint
Fewster, C. J., & Smith, C. J. (2007) · Cited by 1
Grawitacja. Wprowadzenie do ogólnej teorii względności Einsteina
Hartle, J. B. (2010) · Wydawnictwa Uniwersytetu Warszawskiego eBooks · doi:10.31338/uw.9788323519140 · Cited by 1
Electro-Gravity Via Geometric Chronon FieldPreprint
Suchard, E. H. (2014) · viXra · Cited by 1
RDM-stars and related topicsPreprint
Nikitin, I. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.09074 · Cited by 1
“Thus, there is an interesting opportunity to create effectively the matter of negative mass for the needs of the model considered here, as well as for the other models (warp drives [27], wormholes [28], time machines [28]), from ordinary matter, by compressing it to densities higher than the Planck one.”
Assessing Hypothetical Gravity Control PropulsionPreprint
Millis, M. G. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.physics/0603113 · Cited by 1
“Even if used on a rocket, there are a number of different ways to envision applying such an effect, each yielding considerably different conclusions; (1) apply it to the whole rocket system, (2) just to the propellant, (3) just to the vehicle, or (4) just to the expelled propellant.”
InfluentialTime, Closed Timelike Curves and CausalityPreprint
Lobo, F. S. N., & Crawford, P. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0206078 · Cited by 1
“Within the framework of general relativity, it is possible to warp spacetime in a small bubblelike region [11], in such a way that the bubble may attain arbitrarily large velocities, v(t).”
Weak energy condition violation and superluminal travel
Lobo, F. S. N., & Crawford, P. (2002) · CERN Document Server (European Organization for Nuclear Research) · doi:10.48550/arxiv.gr-qc/0204038 · Cited by 1
“However, it moves along a spacetime temporal trajectory, contained within it’s light cone, for light suffers the same distortion of spacetime [3].”
Lobo, M. P. (2020) · doi:10.21428/c53615e7.355f8f7f · Cited by 1
Restoring classical energy conditions at quantized levelPreprint
AlMasri, M. W. (2020) · arXiv (Cornell University) · Cited by 1
Exotic Fluids Matching the Stress-Energy Tensor of Alcubierre Warp Drive SpacetimesPreprint
Béatrix-Drouhet, W. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.09941 · Cited by 1
Investigations into quantum light-matter interactions, their approximations and applications
Funai, N. (2021) · UWSpace (University of Waterloo) · Cited by 1
Glenn, C. M. (2022) · doi:10.36227/techrxiv.19224552.v1 · Cited by 1
Glenn, C. M. (2022) · doi:10.36227/techrxiv.19224552 · Cited by 1
Elasticidade do espaço-tempoPreprint
Lobo, M. P. (2020) · doi:10.31219/osf.io/nbca8 · Cited by 1
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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