WRP-3: No superluminal positive-energy warp drive survives

The live argument, with a dated score: superluminal and positive-energy, none; subluminal and positive-energy, one.

Kind: constraint · Family: WRP (The warp drive class) · Last reviewed: 2026-09-12

The result

Absence as a finding: as of September 2026 no peer-reviewed superluminal positive-energy warp drive has survived review. Lentz's 2021 soliton was found by Santiago, Schuster and Visser never to have solved the Einstein equations, and independently by Celmaster and Rubin (2025) to contain negative-energy regions and derivation errors; Lentz's reply is in conference proceedings and a blog post, not in a refereed paper. Fell and Heisenberg proved positivity for Eulerian observers only. The one surviving positive-energy result, Fuchs et al. (2024), is a constant-velocity subluminal shell. Rodal (2026) is "predominantly positive" and still violates the NEC. Helmerich et al. (2024) state that existing solutions have all required energy-condition violation

What it forbids or costs

The live argument, with a dated score: superluminal and positive-energy, none; subluminal and positive-energy, one

Escape hatches

A future construction outside the Natário class, or a peer-reviewed reply to the objections. Review this entry against the literature every six months

Who it bites

Physics proposals

• VIOLATES: Fell and Heisenberg 2021: positive energy from hidden geometric structure. Recorded in the entry as positivity for Eulerian observers only; not a surviving superluminal positive-energy drive
• VIOLATES: Lentz 2021: hyper-fast positive-energy solitons. The entry's case study: found never to have solved the Einstein equations, then independently found to contain negative-energy regions and derivation errors, with a reply only in proceedings
• DODGES: Warp drives in modified gravity. WRP-3's dated score is implicitly within general relativity. DeBenedictis and Ilijic (2018) is a peer-reviewed superluminal ($v_s = 1.2$) warp drive whose matter satisfies the weak and null conditions, in Einstein-Cartan theory; it evades the score by changing the theory and pays in $10^{68}\,\hbar$ per cubic metre of spin. The register entry should say so.
• SATISFIES: Alcubierre 1994: the warp drive metric. The proposal makes no positive-energy claim; the 1994 letter is where the negative energy requirement was first stated, and the absence WRP-3 records is consistent with it.
• SATISFIES: Bobrick and Martire 2021: physical warp drives. Makes no superluminal positive-energy claim and says its conclusions do not support Lentz's; its subluminal positive-energy idea is carried by the group's own 2024 shell, the one survivor the entry records
• SATISFIES: Fuchs et al. 2024: the constant-velocity physical warp shell. The one surviving positive-energy result the entry records, and it is subluminal and constant-velocity as the entry says
• SATISFIES: Natário 2002: warp drive with zero expansion. No positive-energy claim is made; Theorem 1.7 is a proof that none can be made inside the class in general relativity, consistent with the absence WRP-3 records.
• SATISFIES: Van Den Broeck 1999: the pocket geometry. No positive-energy claim; the paper reduces the negative energy and says so.

Fictional drives

• SILENT: Elite Dangerous: the frame shift drive (Frontier Developments, 2014). The game assumes a working superluminal bubble; the absence WRP-3 records is never engaged.
• SILENT: EVE Online: the warp drive (CCP Games, 2003). The lore asserts a working superluminal bubble sourced by depleted vacuum; the absence WRP-3 records is never engaged.
• SILENT: Futurama: the Planet Express ship's dark matter engines (1999 onward). The show asserts a working superluminal bubble fuelled by dense matter; the absence WRP-3 records is never engaged.
• SILENT: Star Trek: warp drive (1966 onward). The franchise asserts positive-energy superluminal warp by default; the absence WRP-3 records is the absence of any Star Trek answer to it.
• SILENT: Stellaris: warp, hyperlane and wormhole (Paradox Development Studio, 2016). The warp mode asserted a working superluminal bubble; the absence WRP-3 records is never engaged, and the mode itself was removed in 2018 for design reasons.
• SILENT: The Orville: quantum drive (2017 onward). The show asserts a working superluminal bubble sourced by a fuel; the absence WRP-3 records is not engaged in any episode.
• RULE: Death's End: curvature propulsion (Liu Cixin, 2010). The one surviving positive-energy warp result is subluminal and constant-velocity; the novel's drive accelerates to c and stays there, which is the regime WRP-3 permits, by the novel's own rule of never exceeding light.
• RULE: Star Citizen: quantum drive and jump points. The quantum drive claims no superluminal warp, so it sits on the side of the entry's line where a positive-energy result exists; the lore's negative energy is unnecessary by the 2024 result; the lore does not reflect it.

Sources

• Santiago, Schuster and Visser, Phys. Rev. D 105, 064038 (2022); Lentz, Class. Quantum Grav. 38, 075015 (2021), arXiv:2006.07125, and MG16 proceedings (2023), arXiv:2201.00652; Celmaster and Rubin, arXiv:2511.18251 (2025); Fell and Heisenberg, Class. Quantum Grav. 38, 155020 (2021), arXiv:2104.06488; Fuchs et al., Class. Quantum Grav. 41, 095013 (2024), arXiv:2405.02709; Helmerich et al., Class. Quantum Grav. (2024), arXiv:2404.03095; Rodal, Gen. Relativ. Gravit. 58, 1 (2026), arXiv:2512.18008; Le, arXiv:2602.18023 (2026); Barzegar, Buchert and Vigneron, arXiv:2602.16495 (2026) ✓ (2025–2026 preprints ⚠ v1, found by search)