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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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Quantum tunneling and quasinormal modes in the spacetime of the Alcubierre warp drive
Jusufi, K., Sakallı, İ., & Övgün, A. (2017) · General Relativity and Gravitation · doi:10.1007/s10714-017-2330-8 · Cited by 29
Alcubierre, M., & Lobo, F. S. N. (2017) · Fundamental Theories of Physics · doi:10.1007/978-3-319-55182-1_11 · Cited by 27
Self-citationRelativistic Bohmian trajectories of photons via weak measurements
Foo, J., Asmodelle, E., Lund, A. P., & Ralph, T. C. (2022) · Nature Communications · doi:10.1038/s41467-022-31608-6 · Cited by 26
“We finally draw a connection between the relativistic wavefunction and the Alcubierre metric [31], proposing this as a relativistic generalisation to the quantum potential [5] which is usually understood as guiding the particle in the nonrelativistic limit.”
BackgroundMethodBlack holes in a swirling universe
Astorino, M., Martelli, R., & Viganò, A. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.064014 · Cited by 26
Simple and double walled Krasnikov tubes: II. Primordial microtubes and homogenization
Gravel, P. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/4/001 · Cited by 25
Effingham, N. (2020) · doi:10.1093/oso/9780198842507.001.0001 · Cited by 28
Fluid dynamics in the warp drive spacetime geometry
Santos-Pereira, O. L., Abreu, E. M. C., & Ribeiro, M. B. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-08921-3 · Cited by 29
A Discussion of Space-Time Metric Engineering
White, H. G. (2003) · General Relativity and Gravitation · doi:10.1023/a:1026247026218 · Cited by 24
Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime
Yu, H., & Wu, P. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.69.064008 · Cited by 24
QUASIPARTICLE UNIVERSES IN BOSE–EINSTEIN CONDENSATES
Fischer, U. R. (2004) · Modern Physics Letters A · doi:10.1142/s0217732304015099 · Cited by 23
Assessing Potential Propulsion Breakthroughs
Millis, M. G. (2005) · Annals of the New York Academy of Sciences · doi:10.1196/annals.1370.023 · Cited by 23
“The warp drive concept involves moving a bubble of spacetime that carries a vehicle within [Alcubierre 1994].”
InfluentialCausality-violating Higgs singlets at the LHC
Ho, C. M., & Weiler, T. J. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.045004 · Cited by 22
“In chronological order (perhaps not the best listing scheme for CTC proposals), proposals include van Stockum and Tipler’s rotating cylinder [1, 2], Gödel’s rotating universe [3], Wheeler’s spacetime foam [4], Kerr and Kerr-Newman’s black hole event horizon interior [5], Morris, Throne and Yurtsever’s traversable worm…”
A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation
Ahmed, F. (2017) · Communications in Theoretical Physics · doi:10.1088/0253-6102/68/6/735 · Cited by 22
Alcubierre warp drive: On the matter of matter
McMonigal, B., Lewis, G. F., & O’Byrne, P. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.064024 · Cited by 22
Dust content solutions for the Alcubierre warp drive spacetime
Santos-Pereira, O. L., Abreu, E. M. C., & Ribeiro, M. B. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-8355-2 · Cited by 25
“Alcubierre also stated [1] that the warp drive is possible without the use of non trivial topologies, such as wormholes.”
BackgroundMethodInfluentialMars, M., Mena, F. C., & Vera, R. (2013) · General Relativity and Gravitation · doi:10.1007/s10714-013-1574-1 · Cited by 21
“This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].”
Four-dimensional non-linear ray tracing as a visualization tool for gravitational physics
Weiskopf, D. (2002) · Visualization · doi:10.1109/visual.2000.885728 · Cited by 21
Making the universe safe for historians: Time travel and the laws of physics
Woodward, J. F. (1995) · Foundations of Physics Letters · doi:10.1007/bf02187529 · Cited by 20
Hyopthetical Gravity Control and Possible Influence on Space Propulsion
Tajmar, M., & Orfeu Bertolami, A. (2005) · Journal of Propulsion and Power · doi:10.2514/1.15240 · Cited by 21
Effingham, N. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780198842507.003.0005 · Cited by 19
Pure radiation metric with stable closed timelike curves
Sarma, D., Patgiri, M., & Ahmed, F. (2013) · General Relativity and Gravitation · doi:10.1007/s10714-013-1633-7 · Cited by 20
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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