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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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“Concerning the propulsion principle of field propulsion system, the distribution of a typical field as shown in Figure 1 is fundamental; accordingly, several kinds of propulsion systems have been proposed, that is, 1) Space Drive Propulsion System (Minami, 1988, 1994, 1997, 1998), 2) Superstring-Based Field Propulsion…”
MethodMinami, Y. (2005) · AIP conference proceedings · doi:10.1063/1.1867273 · Cited by 3
“1) Space Drive Propulsion System (Minami, 1994, 1997, 1998), 2) Superstring-Based Field Propulsion (Minami, 2004), 3) ZPF (Zero Point Field) Propulsion System (Froning and Barrett, 1998), 4) Alcubierre’s Warp Drive Propulsion System (Alcubierre, 1994).”
BackgroundEnergy density-flux correlations in an unusual quantum state and in the vacuum
Ford, L. H., & Roman, T. A. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.064012 · Cited by 3
Inertia reduction - and possibly impulsion - by conditioning electromagnetic fields
H. Froning, Jr., & Barrett, T. W. (1997) · AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit · doi:10.2514/6.1997-3170 · Cited by 3
Faster-than-Light Approaches in General Relativity
(2009) · American Institute of Aeronautics and Astronautics eBooks · doi:10.2514/5.9781563479953.0471.0507 · Cited by 3
“This quantity is defined as [5]:”
BackgroundMethodInfluentialGalaxy travel via Alcubierre's warp drive
Fil’chenkov, M. L., & Laptev, Y. P. (2017) · Acta Astronautica · doi:10.1016/j.actaastro.2017.07.011 · Cited by 3
Localized thermal states and negative energy
Rosso, F. (2019) · Journal of High Energy Physics · doi:10.1007/jhep10(2019)246 · Cited by 3
The Artificial Inducement of a Local Space Warp Bubble Using a VEM Drive.
Pares, D. P., Judah, M., & Finley, K. (2018) · AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit · doi:10.2514/6.2018-4633 · Cited by 3
“…(RF) resonant, variable near field reactants, VEM Drive, EM Drive The Artificial Inducement of a Local Space Warp Bubble Using a VEM Drive Alcubierre (1994), Van den Broeck (1999), Obousy and Cleaver (2007) expound the possibility of faster than light travel using the theoretical concept…”
BackgroundMethodInfluentialInvestigation into Compactified Dimensions: Casimir Energies and Phenomenological AspectsPreprint
Obousy, R. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0901.3640 · Cited by 3
Froning, H. D. (2000) · AIP conference proceedings · doi:10.1063/1.1290903 · Cited by 3
On a macroscopic traversable spacewarp in practicePreprint
Mansouryar, M. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0511086 · Cited by 7
“, WD metric [78] can cause better results.”
Wei-Xing, S., Pun-Xun, W., & Yu, H. (2003) · Chinese Physics Letters · doi:10.1088/0256-307x/20/12/005 · Cited by 3
Lower Bounds on Negative Energy Densities for the Scalar Field in Flat Spacetime
Wei-Xing, S., Yu, H., Ren, Z., Wu, P., & Li, F. (2006) · Chinese Physics Letters · doi:10.1088/0256-307x/23/1/008 · Cited by 3
Toward an Interstellar Mission: Zeroing in on the Zero-Point-Field Inertia ResonancePreprint
Haisch, B., & Rueda, A. (1999) · Cited by 3
Advanced Propulsion: Pulsed, Fusion, Antimatter and Breakthrough Physics
Howe, S. D. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-819725-7.00022-2 · Cited by 3
A new theory of tensor-scalar gravity coupled to Aharonov—Bohm electrodynamics
Minotti, F. O., & Modanese, G. (2025) · Modern Physics Letters A · doi:10.1142/s0217732325500233 · Cited by 2
“In this respect, it is important to recall that the speed is measured in the Minkowski flat space-time background,”
Sculpting Spacetime: Thin Shells in Wormhole Physics
Lobo, F. S. N. (2025) · Universe · doi:10.3390/universe11080270 · Cited by 2
Parsons, P. (1996) · Science · doi:10.1126/science.274.5285.202 · Cited by 2
STATIC AND DYNAMIC TRAVERSABLE WORMHOLES
Adamiak, J. (2008) · The Ninth Marcel Grossmann Meeting · doi:10.1142/9789812834300_0357 · Cited by 2
Ahmed, F., Hazarika, B. B., & Sarma, D. (2020) · Advances in High Energy Physics · doi:10.1155/2020/8265872 · Cited by 2
Billiard-ball paradox for a quantum wave packet
Bishop, L. G., Ralph, T. C., & Costa, F. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac8198 · Cited by 2
Segman, Y. J. (2022) · Natural Science · doi:10.4236/ns.2022.147026 · Cited by 2
“Alcubierre introduces warp drive bubble [3, 6, 7].”
Warp Factory: A Numerical Toolkit for the Analysis and Optimization of Warp Drive Geometries
Helmerich, C., Fuchs, J., Bobrick, A., Sellers, L., Dangelo, S., Martire, G., & Agnew, J. F. (2023) · AIAA SciTech Forum · doi:10.2514/6.2023-0553 · Cited by 2
Newtonian Forces Exerted by Electromagnetic Waves Traveling into Matter
Funaro, D. (2023) · International Journal of Theoretical Physics · doi:10.1007/s10773-023-05491-w · Cited by 2
“They rely on modifications of the space-time and involve superluminal velocities (see the device proposed by M. Alcubierre [24]).”
Falling into the Past: Geodesics in a Time Travel Metric
MacLaurin, C., Costa, F., & Ralph, T. C. (2024) · Universe · doi:10.3390/universe10020095 · Cited by 2
“Alcubierre [16] starts with coordinates ( t , x , y , z ) on a manifold, and a path x s ( t ) along the x -axis, where the “s” stands for spaceship.”
BackgroundInfluentialHuey, G. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad4e00 · Cited by 2
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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