Warp drives and closed timelike curves
Open accessAbstract
It is commonly accepted that superluminal travel may be used to facilitate time travel. This is a purely special-relativistic argument, using the fact that for observers in two frames of reference, separated by a spacelike interval, the non-causal (spacelike) future of one observer includes part of the causal past of the other. In this paper we provide a concrete realization of this argument in a curved general-relativistic spacetime, using warp drives as the means of faster-than-light travel. By generalizing the usual warp drive metric to allow for a non-unit lapse function, we allow the warp drive to switch between reference frames in a purely geometric way. With an additional modification allowing the warp drive to have compact support, this permits us to glue two warp drives together to construct a closed timelike geodesic, such that a test particle following the geodesics of the two warp drives travels back to its own past. This provides a precise mathematical model for the connection between faster-than-light travel and time travel in general relativity, and the first such model to be explicitly formulated using two warp drives. We also give a detailed discussion of weak energy condition violations in the non-unit-lapse warp drive.
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The warp drive spacetime constructed here is a new type of warp drive beyond the Natario class and hence not subject to the same scope discussed in [9] and [18] due to its use of modified spatial terms in the metric.
“Moreover, the warp drive spacetime constructed here is a new type of warp drive beyond the Natario class and hence not subject to the same scope discussed in [9] and [18] due to its use of modified spatial terms in the metric.”
From Constant velocity physical warp drive solution (2024) · cites this paper as [18]
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Cites
The warp drive: hyper-fast travel within general relativity
Alcubierre, M. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/5/001 · Cited by 569 · cited 5× · see citing works
“The most notable are their seemingly-inevitable violation of the energy conditions [5, 6], the typically vast amounts of (negative) energy required to sustain them [1, 7], and the formation of event horizons [1, 8].”
InfluentialCuriel, E. (2017) · Einstein Studies · doi:10.1007/978-1-4939-3210-8_3 · Cited by 226 · see citing works
Superluminal Travel Requires Negative Energies
Olum, K. D. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3567 · Cited by 126 · see citing works
Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory
Lentz, E. W. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abe692 · Cited by 50 · see citing works
Introducing physical warp drives
Bobrick, A., & Martire, G. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abdf6e · Cited by 45 · see citing works
Generic warp drives violate the null energy condition
Santiago, J., Schuster, S., & Visser, M. (2022) · Physical Review D · doi:10.1103/physrevd.105.064038 · Cited by 42 · cited 10× · see citing works
“The most notable are their seemingly-inevitable violation of the energy conditions [5, 6], the typically vast amounts of (negative) energy required to sustain them [1, 7], and the formation of event horizons [1, 8].”
BackgroundMethodInfluentialPositive energy warp drive from hidden geometric structures
Fell, S. D. B., & Heisenberg, L. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac0e47 · Cited by 22 · see citing works
Flagged first, then by citations
Research works printed but not linked: 14
- Barak Shoshany. Lectures on Faster-than-Light Travel and Time Travel. SciPost Phys. Lect. Notes, 10, 2019. arXiv:1907.04178, doi:10.21468/SciPostPhysLectNotes.10. · DOI
- Francisco S. N. Lobo, editor. Wormholes, Warp Drives and Energy Conditions. Springer International Publishing, 2017. doi:10.1007/978-3-319-55182-1. · DOI · Paper page
- Serguei Krasnikov. Back-in-Time and Faster-than-Light Travel in General Relativity. Springer Interna- tional Publishing, 2018. doi:10.1007/978-3-319-72754-7. · DOI
- Chris Van Den Broeck. A 'warp drive' with more reasonable total energy requirements. Classical and Quantum Gravity, 16(12):3973-3979, 1999. doi:10.1088/0264-9381/16/12/314. · DOI · Paper page
- Pedro F. González-Díaz. Warp drive space-time. Physical Review D, 62(4), 2000. doi:10.1103/ physrevd.62.044005. · DOI
- Allen E. Everett. Warp drive and causality. Phys. Rev. D, 53:7365-7368, 1996. URL: https: //link.aps.org/doi/10.1103/PhysRevD.53.7365, doi:10.1103/PhysRevD.53.7365. · DOI · Paper page
- Francisco S. N. Lobo. Closed timelike curves and causality violation. 2010. URL: https://arxiv. org/abs/1008.1127, doi:10.48550/ARXIV.1008.1127. · DOI
- Jacob Hauser and Barak Shoshany. Time Travel Paradoxes and Multiple Histories. Phys. Rev. D, 102, Sep 2020. arXiv:1911.11590, doi:10.1103/PhysRevD.102.064062. · DOI
- Barak Shoshany and Jared Wogan. Wormhole Time Machines and Multiple Histories. Gen. Relativ. Gravit., 55(44), 2023. arXiv:2110.02448, doi:10.1007/s10714-023-03094-8. · DOI
- Barak Shoshany and Zipora Stober. Time Travel Paradoxes and Entangled Timelines. 2023. arXiv:2303.07635, doi:10.48550/arXiv.2303.07635. · DOI
- Barak Shoshany. OGRe: An Object-Oriented General Relativity Package for Mathematica. Journal of Open Source Software, 6(65):3416, 2021. doi:10.21105/joss.03416. · DOI
- Barak Shoshany. OGRePy: An Object-Oriented General Relativity Package for Python. 2024. arXiv:2409.03803, doi:10.48550/arXiv.2409.03803. · DOI
- José Natário. Warp drive with zero expansion. Classical and Quantum Gravity, 19(6):1157-1165, 2002. doi:10.1088/0264-9381/19/6/308. · DOI · Paper page
- Martin Bojowald. Hamiltonian formulation of general relativity, pages 17-112. Cambridge University Press, 2010. doi:10.1017/CBO9780511921759.003. · DOI
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Constant velocity physical warp drive solution
Fuchs, J., Helmerich, C., Bobrick, A., Sellers, L., Melcher, B., & Martire, G. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad26aa · Cited by 11 · see citing works
- Authors
- Shoshany, B., & Snodgrass, B.
- Affiliations
- Brock University (CA)
- University of Cambridge (GB)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2024-09-16
- Volume
- 41
- Issue
- 20
- Pages
- 205005
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W4401936449
- Cited by
- 6
- References
- 7
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 2
- FWCI
- 1.13
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Mitacs (Globalink Research Internship)
- 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 › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- warp drive, closed timelike curves, time travel, superluminal travel, weak energy condition violation
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