Radiative Signatures from Warp Drives Traveling Through the Earth's Atmosphere

Abraham Loeb; Shaun David Brocus Fell

REVIEW 4 major objections 5 minor 51 references

Radiative Signatures from Warp Drives Traveling Through the Earth's Atmosphere

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read An aircraft-scale warp bubble moving through Earth's atmosphere at relativistic speed would produce a luminous gamma-ray and optical signature, with radiated power from tens of terawatts to tens of exawatts.

desk verdict A transparent GRHD simulation of Alcubierre warp bubbles in air; the terawatt-luminosity claim follows from the simulated shock zone, though the fixed-background assumption and lack of code/data keep it from a clean accept. read the letter →

arxiv 2608.10800 v1 pith:P7FPXFMK submitted 2026-08-11 gr-qc hep-ph

Shaun David Brocus Fell , Abraham Loeb This is my paper · ORCID

classification gr-qchep-ph

keywords warpdriveAlcubierrespacetimezero-ADM-massspacetimesgeneralrelativistichydrodynamicsatmosphericbowshockbremsstrahlunggamma-raysignaturesRankine-Hugoniotconditions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

An aircraft-scale warp bubble moving through Earth's atmosphere at relativistic speed would be glaringly observable. Numerical simulations of an Alcubierre-type, zero-ADM-mass spacetime (one with vanishing total gravitational mass) show that air piles up into a detached bow shock; the post-shock gas reaches tens to hundreds of MeV per nucleon and radiates free-free power between roughly $10^{13}$ and $10^{19}$ watts, concentrated in gamma rays and hard X-rays. A ground observer would see both a bright high-energy source and, because the atmosphere absorbs the hardest photons and re-radiates them, a glowing stratospheric patch. This matters because it turns warp-drive proposals into concrete search targets and implies that any relativistic warp-drive transit through the atmosphere would leave a 'unique brilliant glow' that existing unidentified anomalous phenomena (UAP) detections do not show.

What carries the argument

The central object is a zero-ADM-mass warp bubble: an Alcubierre-type spacetime whose curvature is confined to a thin shell, so that to the atmosphere it acts like a blunt obstacle moving through the air. The fluid is evolved with flux-conservative general-relativistic hydrodynamics on this fixed, stationary metric, and a shock-capturing scheme resolves the detached bow shock. The analytical backbone is the relativistic Rankine-Hugoniot jump conditions, which fix post-shock temperature, compression ratio, and shock standoff distance from the Lorentz factor and upstream state alone; a simple mass-conservation argument gives the standoff distance $\Delta/R\sim \rho_1/(2C\rho_2)$. The luminosity is then computed by integrating free-free bremsstrahlung from the hot, non-equilibrated electron population over the shocked volume, using measured electron-heating fractions and air-fluorescence efficiency for the re-radiated glow.

What would settle it

A simulation that includes the Alcubierre source term and allows metric backreaction from the shocked air would settle the matter: if the detached bow shock and the $10^{13}$--$10^{19}$ W free-free luminosity do not survive the coupling, the predicted signature is an artifact of the fixed-metric approximation. A complementary check is to search gamma-ray and air-fluorescence data for a compact, fast-moving, short-lived source with a 0.1--100 MeV spectrum and an accompanying optical/UV stratospheric glow; a long null search would put an upper limit on the rate of such transits.

Watch

Extended reading notes

Core claim

The paper's central claim is that zero-ADM-mass warp-drive spacetimes, the class that includes the Alcubierre metric and other zero-ADM-mass warp geometries, interacting with air at bubble speeds between $0.1c$ and $0.75c$ produce a standing relativistic bow shock whose radiative output exceeds one terawatt and reaches tens of exawatts for the fastest, largest cases. The stagnation temperature behind the shock is set by the Lorentz factor alone, $k_B T_{\rm stag}\sim(W_1-1)m_u c^2$, reaching about 144 MeV at $0.5c$ and far beyond the pion threshold at $0.75c$. Electrons and ions do not equilibrate on the flow time, so the electrons carry only a fraction of the ion temperature, yet their free-free emission dominates the total luminosity. The authors also show that the high-Mach-number limit is equivalent to the cold-gas limit up to an order-one coefficient, so warm, inexpensive simulations describe the cold atmosphere, and they derive scaling laws $L\propto \rho_1^2 R^3$ and $L\propto v_s^3$ above the relativistic-enhancement knee, with a low-luminosity floor near $10^3$ W for a micron-scale bubble at sea-level density. The conclusion is that relativistic, aircraft-scale warp-drive activity in the atmosphere is observationally loud, while compact or subsonic configurations would not glow by this mechanism.

Load-bearing premise

The calculation treats the warp bubble's metric as fixed and ignores the exotic-matter source that would generate it, letting air stream through the wall on the assumption that the stagnation zone and shock sit entirely outside it; if that source couples to normal matter or if the shocked air backreacts on the geometry, the standoff distance, compression, and luminosity could all change.

Editorial extensions

If this is right

A relativistic warp-drive transit through Earth's atmosphere at speeds above roughly $0.1c$ would not be stealthy: total radiated power lies between $10^{13}$ and $10^{19}$ W for aircraft-scale bubbles.
Ground observers would register two signals at once: a direct gamma-ray/hard-X-ray flash from the shock and a visible stratospheric glow from re-radiation of absorbed photons.
Observed UAP luminosities are orders of magnitude below the predicted values, so the mechanism sets an upper limit on how often relativistic aircraft-scale warp bubbles could pass through the atmosphere unnoticed.
The luminosity scales as $L\propto \rho_1^2 R^3$ and, above the relativistic-enhancement knee, as $L\propto v_s^3$; compact, slow, or micron-scale bubbles fall below the glow threshold, limiting the constraints to the relativistic, aircraft-scale regime.
The quantitative results apply to zero-ADM-mass metrics of the type exemplified by the Alcubierre spacetime; metrics with non-zero ADM mass would have different curvature falloff and hence different shock structure and luminosity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the paper argues the shock is controlled mainly by relative velocity rather than by metric details, the same gamma-ray-plus-glow signature should be generic to any zero-ADM-mass bubble with an exponentially flat exterior, not just the specific tanh shape simulated.
Existing gamma-ray transient monitors and air-fluorescence detectors could be searched for compact, fast-moving sources; a null search would extend the paper's constraint backward in time without any new instrument.
The optically thin assumption may break down for deeper, denser atmospheric passages, where pair production could form an optically thick fireball and make the signature even brighter and spectrally harder; that regime is not computed here.
The absence of a luminous glow would not rule out warp-drive technology in general: subsonic, small, or otherwise sub-hydrodynamic bubbles would produce no detached shock, so their detection would require kinetic plasma modeling rather than this shock-based channel.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is the first GRHD simulation of a warp bubble moving through air, and it produces a concrete, order-of-magnitude prediction—aircraft-scale Alcubierre bubbles at v > 0.1c would radiate at terawatt to exawatt levels, mostly in gamma rays. That is a genuinely new number for a previously qualitative question, and the paper's transparency is a real virtue: they describe the code modifications (including a fallback entropy-advection scheme for cold cells), run convergence checks on the Bernoulli invariant and the mass-flux residual, and explicitly flag every major caveat.

The simulation itself looks sound for what it claims. The luminosity is integrated directly from the simulated shocked-fluid state via a standard free-free emissivity, not from the fitted standoff model. The analytic standoff curves in Fig. 3 are partly fits—the O(1) constant C is calibrated to all runs—but that doesn't contaminate the simulated luminosity, which is the load-bearing claim. The stress-test note worries about impermeable vs. permeable wall; I don't think that lands. The simulation naturally allows fluid to cross the wall; the shock standoff is whatever the metric produces. The solid-body analog is only an interpretive aid, and the calibration absorbs the difference.

The real soft spots are three. First, the metric is prescribed and the source term is ignored. That's a standard test-fluid approximation, but it deserves more than an assertion; the claim that the source has little impact on the shock is plausible (the shock sits in the far field of the wall) but not demonstrated. Second, no code or data is released, so the convergence analysis and the specific numbers cannot be independently reproduced—unfortunate for such a claim. Third, the relativistic enhancement factor in the emissivity is a crude fit, and the electron heating fraction xi is borrowed from PIC simulations of unmagnetized relativistic shocks; bracketing xi from 0.1 to 0.5 shifts the luminosity by a factor of a few, which is within the claimed order-of-magnitude but should be shown.

Overall, the terawatt claim is robust within the stated model. This is a speculative paper, but it is technically competent and honest about its limits. A serious referee should see it—it deserves a chance to be fixed and published, not desk-rejected.

Referee Report

4 major / 5 minor

Summary. The paper models the interaction of a static Alcubierre-type warp metric with a uniform, unmagnetized, perfect-fluid atmosphere using the Athena++ GRHD code with AMR, a Taub-Mathews equation of state, and a custom conservative-to-primitive fallback based on an advected entropy invariant. It computes the steady-state bow shock standoff, compression ratio, and post-shock electron temperature, then post-processes free-free bremsstrahlung luminosities from a two-temperature (electron/ion) description. The main claim is that an aircraft-scale (R=25-100 m) bubble moving at 0.1-0.75c through the atmosphere produces 10^13-10^19 W of gamma/X-ray emission plus a bright stratospheric re-radiation glow, providing an observational signature for terrestrial warp-drive activity.

Significance. If the central claim survives scrutiny, the paper is significant because it converts an exotic-propulsion speculation into a falsifiable set of atmospheric observables: a point-like gamma/hard-X-ray source and a visible stratospheric glow. The numerical infrastructure is a strength: the paper gives a detailed, physically motivated shock-capturing scheme, a careful treatment of the con2prim problem in cold high-Mach flows, and two convergence diagnostics (mass-flux residual and Bernoulli invariant). The radiative calculation is transparent, and the optical-depth check supports the optically-thin assumption. However, the quantitative headline depends on an unspecified density normalization and on a wall-permeability assumption that is not tested, so the significance is conditional on those two points being resolved.

major comments (4)

[Section III and Eqs. (43)-(45)] The physical normalization of the fluid density is never specified. The initial condition is given as rho_inf=1 in code units, but the conversion to kg m^-3 is absent, so the quoted luminosities in watts and kinetic powers in watts cannot be reproduced. The optical-depth example in Sec. II G1 uses n_e=7.6e20 m^-3 (roughly 70 km altitude), while the observer calculations in Sec. III assume a source at 100 km. Since L scales as rho^2, choosing sea-level instead of 100-km density changes L by many orders of magnitude and can move the 'exceeding one terawatt' claim below threshold. Please state the assumed atmospheric density profile and report L for representative altitudes.
[Sec. II A and Eq. (19)] The simulation explicitly lets the fluid pass through the warp wall, while the analytic standoff model in Eq. (19) conserves mass by draining shocked gas tangentially with zero through-wall flux. The paper asserts that the spacetime source term has 'little impact on the shock properties' but gives no test of this claim. Because the fitted coefficient C in Eq. (19) is calibrated against the permeable simulation, the analytic curves in Figs. 3 and 4 cannot distinguish a transparent wall from an opaque one, and the luminosity integral (44) inherits this uncertainty through the shock volume. Add a control simulation with an impermeable spherical wall (or otherwise couple the metric source to the fluid) and show that the standoff and L are unchanged.
[Sec. II G4, Eq. (43)] The multiplicative factor (1+4.4e-10 T_e) is a low-temperature relativistic correction, but it is applied at T_e up to roughly 10^12 K (v=0.75c, xi=0.2). In this regime the linear-in-T correction is not a valid approximation to the thermal bremsstrahlung emissivity; the high-velocity luminosities (up to tens of exawatts) may be substantially over- or under-estimated. Please replace it with a relativistic thermal bremsstrahlung formula valid at k_B T_e >> m_e c^2, or explicitly bound the error.
[Sec. II G2 and Figs. 4-5] The electron heating fraction is fixed at xi=0.2 in the post-processing, although the text gives a bracket xi in [0.1,0.5] from PIC simulations. Since the bremsstrahlung luminosity scales as T_e^1 to T_e^{3/2} depending on the regime, this choice introduces a factor of 3-10 uncertainty in L. The quoted ranges (10^13 to 10^19 W) should include this systematic uncertainty, and the 'exceeding one terawatt' statement should be re-evaluated at the lower end of the bracket.

minor comments (5)

[Sec. II G1] There is a typo: 'computated' should be 'computed'. Also, the optical-depth example would be clearer if the assumed altitude were stated alongside the fiducial n_e value.
[Sec. II G3] The statement 'k_B T_e about 0.625 MeV at v=0.1c' appears inconsistent with Eq. (15) and the stated xi=0.2; please clarify which value of the heating fraction is used here.
[Sec. V] The extrapolation to micron-scale bubbles and the 10^3 W luminosity floor goes well beyond the simulated parameter range; it should be labeled as a heuristic scaling rather than a quantitative prediction.
[General] No data or code availability statement is provided. Releasing the Athena++ input files and the post-processing scripts would materially improve reproducibility of the quantitative claims.
[Sec. II G2] The two-temperature model appears to be implemented as post-processing rather than as an evolved sector of the GRHD simulation; the paper should state this explicitly to avoid confusion.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor calibrated standoff constant disclosed; central luminosity result is computed from simulation and is not circular.

fitted input called prediction [Sec. III, Fig. 3 and Sec. II E, Eq. (19)]
"The O(1) constant is calibrated against all runs at once such that a single constant feeds into all analytic predictions for the standoff distance."

Eq. (19) contains the O(1) coefficient C, and the text states C is calibrated against all simulation runs in Fig. 3. The 'analytic predictions' for standoff therefore are not independent first-principles results; they are fits to the same data they are plotted against. This is a minor, disclosed calibration: the paper's headline luminosity is not taken from this fitted curve but is integrated directly from the simulated fluid state via Eq. (44), so the central radiative claim does not reduce to the fitted constant.

full rationale

The derivation chain for the main luminosity result is self-contained: the GRHD simulation evolves the Alcubierre metric with the Valencia conserved formulation, the post-shock state is checked against Rankine-Hugoniot jump conditions, and the luminosity is computed from the standard free-free emissivity (Eqs. 42-44) integrated over the simulated shock zone. The only fitted element is the O(1) standoff coefficient C in Eq. (19), which is explicitly disclosed as calibrated and affects only the analytic standoff comparison, not the simulated luminosity. The paper does not invoke any load-bearing self-citation, uniqueness theorem, or ansatz disguised as a citation. The impermeable-wall versus permeable-wall modeling concern is a physical correctness risk, not a circularity: the simulation itself does permit fluid passage, and the luminosity is measured from that simulation. Overall, no significant circularity; the minor calibrated constant warrants a low non-zero score.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central simulation uses the Alcubierre metric with shape parameters R and sigma. It relies on the idealization of a static spacetime with no coupling to the exotic source, and on a high-Mach/cold-gas equivalence to map warm-proxy runs onto the cold atmosphere. The luminosity post-processing uses an electron heating fraction xi selected from the literature and a calibrated standoff constant C, plus an unstated temperature cutoff in the shock-zone integration.

free parameters (2)

Standoff coefficient C = not quoted; calibrated over all runs
O(1) constant in the analytical standoff-distance formula (Eq. 19), fit to the simulation data shown in Fig. 3.
Electron heating fraction xi = 0.2 (bracket 0.1-0.5)
Fraction of shock dissipated energy given to electrons; chosen from PIC shock literature and fixed to 0.2 for luminosity post-processing (Sec. II G 2).

assumptions (4)

domain assumption The Alcubierre metric represents a zero-ADM-mass warp drive, and shock structure is roughly independent of the fine geometry for this class.
Used to choose the metric in Sec. II A and to generalize results to other zero-ADM-mass warp metrics.
ad hoc to paper The background metric is static over the simulation and the spacetime source term is neglected; the fluid can pass through the bubble wall without coupling to the source.
Stated in Sec. II A; the authors argue the stagnation zone and shock sit outside the wall, but the interaction with the warp-drive matter is not modeled.
domain assumption Results from warm upstream runs (Theta_1 ~ 10^-3 to 10^-6) apply to the real cold atmosphere (Theta_1 ~ 10^-13) in the high-Mach limit with O(1) accuracy.
Used to make simulations feasible; derived from RH jump conditions in Sec. II E, but relies on the validity of that expansion.
domain assumption The shocked gas is a two-temperature optically thin plasma described by the Taub-Mathews EoS; pair production and pion production do not affect the dynamics.
Assumed in Secs. II C and II G; the paper shows optical depth is small and electron-ion equilibration is slow, but does not quantitatively model pion/neutrino losses.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Radiative Signatures from Warp Drives Traveling Through the Earth's Atmosphere." pith.science (2026). https://pith.science/paper/P7FPXFMK

@misc{pith2026260810800,
  author       = {Pith},
  title        = {Pith review of: Radiative Signatures from Warp Drives Traveling Through the Earth's Atmosphere},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P7FPXFMK}},
  note         = {Machine review of arXiv:2608.10800}
}

read the original abstract

We investigate the observable signatures of zero ADM mass warp drive spacetimes traversing Earth's atmosphere. Numerical simulations indicate that an aircraft-scale spacetime bubble moving at relativistic velocities would have a pronounced observational signature, where interaction with the atmosphere can produce luminosities exceeding one terawatt. The signature of a spacetime bubble at rest or moving at low velocity relative to the Earth would not generate such extreme luminosities. These results establish observational constraints on spacetime-based propulsion operating within the terrestrial environment and provide a framework for identifying potential high-velocity signatures. In particular, a warp drive traveling through the atmosphere at speeds exceeding approximately 10% of the speed of light would produce a unique brilliant glow.

Figures

Figures reproduced from arXiv: 2608.10800 by the authors.

**Figure 2.** FIG. 2. Snapshot of a stabilized simulation showcasing the fluid velocity norm in the warp bubble comoving frame. The [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** FIG. 3. Fractional shock-front standoff relative to the bubble radius, Eq. (19). Simulated data is displayed by the individual [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Total luminosity from [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: FIG. 5. Displayed is the [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: FIG. 6. Maximum compression ratio of the post-shock fluid to the upstream fluid, [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: FIG. 7. Convergence figures of merit for 3 chosen simulation runs, with varying levels of computational challenge. The most [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 34 canonical work pages

[1]

Precisely,C A|v1→0 = 2.7 andC A|v1→1 = 3 2

By simply computing the two limitsv 1 →0 andv 1 →1, one finds thatC A is bounded from below and above by anO(1) constant. Precisely,C A|v1→0 = 2.7 andC A|v1→1 = 3 2 . Thus,δbehaves like∼ 1 M2 with an order 1 coefficient. This cold-limit/high Mach-number equivalence also holds for the other fluid quantities. This implies that large Mach numbers correspond ...

work page
[2]

To high accuracy, most of the thermodynamic quantities are just algebra or cal- culus on the primitives through the EoS

Optical Depth A large amount of the science does not need explicit evolution during the simulation. To high accuracy, most of the thermodynamic quantities are just algebra or cal- culus on the primitives through the EoS. One of the most 6 important ones is the optical depth of the fluid. For the discretized grid, the Thomson optical depth is τT =σ T X xi≥...

work page
[3]

Interaction Timescale The second defining quantity that determines whether the derived quantities can be computed in post- processing is the relation between the interaction timescale of the fluid constituents relative to the flow timescale. The ratio of the interaction timescale to the flow timescale is tei tf low = r π 2 mi me (Θe + Θi)3/2vs Zln Λ(n eσT...

work page
[4]

Whether the pairs stay as tracer objects or cascade into an optically-thick fireball is the single qualitative question about the interaction’s appearance

Pair Production The post-shock energy budget exceeds the pair thresh- old by two orders of magnitude, so electron-positron pairs inevitably form. Whether the pairs stay as tracer objects or cascade into an optically-thick fireball is the single qualitative question about the interaction’s appearance. Thermal pair production switches on when the Wien tail ...

work page
[5]

Luminosity Free-free emission from the hot electrons has a frequency-dependent emissivity. For a non-relativistic Maxwellian, the power per unit volume is dE dtdV = 2πkBTe 3me 1/2 25πe6 3hpmec3 ¯gB X s Z 2 s nsne (42) where ¯gB is the frequency average of the velocity aver- aged Gaunt factor,m e is the electron mass,h p is the planck constant, and whereEi...

work page
[6]

The Code The deployed code heavily utilizes Athena++, an adaptive mesh refinement-based code for magnetohydro- dynamical simulations in special and general relativ- ity [28]. It fits well for this problem, since the back- ground spacetime is non-linear, stationary, and the only dynamical object is the relativistic unmagnetized fluid interacting with the c...

work page
[7]

E. W. Lentz, Classical and Quantum Gravity38, 075015 (2021), arXiv:2006.07125 [gr-qc]

arXiv 2021
[8]

Bobrick and G

A. Bobrick and G. Martire, Classical and Quantum Grav- ity38, 105009 (2021)

work page 2021

Show all 51 references

[9]

S. D. B. Fell and L. Heisenberg, Classical and Quantum Gravity38, 155020 (2021), arXiv:2104.06488 [gr-qc]

2021 arXiv
[10]

Santiago, S

J. Santiago, S. Schuster, and M. Visser, Physical Review D105, 064038 (2022), arXiv:2105.03079 [gr-qc]

2022 arXiv
[11]

Schuster, J

S. Schuster, J. Santiago, and M. Visser, General Rela- tivity and Gravitation55, 14 (2023), arXiv:2205.15950 [gr-qc]

2023 arXiv
[12]

Helmerich, J

C. Helmerich, J. Fuchs, A. Bobrick, L. Sellers, B. Melcher, and G. Martire, Classical and Quantum Gravity41, 095009 (2024), arXiv:2404.03095 [gr-qc]

2024 arXiv
[13]

Helmerich, J

C. Helmerich, J. Fuchs, A. Bobrick, B. Melcher, L. Sell- ers, and G. Martire, inAIAA SCITECH 2023 Forum (2024) arXiv posted 2024; presented at AIAA SciTech 2023, arXiv:2404.10855 [gr-qc]

2024 arXiv
[14]

Fuchs, C

J. Fuchs, C. Helmerich, A. Bobrick, L. Sellers, B. Melcher, and G. Martire, Classical and Quantum Gravity41, 095013 (2024), arXiv:2405.02709 [gr-qc]

2024 arXiv
[15]

Celmaster and S

B. Celmaster and S. Rubin, arXiv e-print (2025), preprint; no journal reference as of 2026-07-01, arXiv:2511.18251 [gr-qc]

2025
[16]

Barzegar, T

H. Barzegar, T. Buchert, and Q. Vigneron, arXiv e-print (2026), preprint; no journal reference as of 2026-07-01, arXiv:2602.16495 [gr-qc]

2026
[17]

Clough, T

K. Clough, T. Dietrich, and S. Khan, The Open Jour- nal of Astrophysics7, 10.33232/001c.121868 (2024), arXiv:2406.02466 [gr-qc]

2024 arXiv
[18]

Barcel´ o, V

C. Barcel´ o, V. Boyanov, L. J. Garay, E. Mart ´ ın-Mart ´ ınez, and J. M. S´ anchez Vel´ azquez, Journal of High Energy Physics08, 288 (2022), arXiv:2207.06458 [gr-qc]

2022 arXiv
[19]

S. Bian, Y. Wang, Z. Wang, and M. Zhu, The European Physical Journal C82, 10.1140/epjc/s10052-022-10840- w (2022), arXiv:2201.06371 [gr-qc]

2022 arXiv
[20]

E. W. Lentz and R. C. Felton, arXiv e-print (2024), preprint (report no. PNNL-SA-198722); no journal refer- ence as of 2026-07-01, arXiv:2405.19381 [astro-ph.IM]

2024 arXiv
[21]

Sellers, A

L. Sellers, A. Bobrick, G. Martire, M. Andrews, and M. Paulini, arXiv e-print (2022), preprint; no journal ref- erence as of 2026-07-01, arXiv:2212.02065 [astro-ph.IM]

2022 arXiv
[22]

Kuwahara and K

S. Kuwahara and K. Cannon, arXiv e-print (2023), preprint; LIGO/Virgo/KAGRA O3 search for super- luminal-source GW bursts. No journal reference as of 2026-07-01, arXiv:2310.16067 [gr-qc]

2023 arXiv
[23]

Clark, W

C. Clark, W. A. Hiscock, and S. L. Larson, Classical and Quantum Gravity16, 3965 (1999), arXiv:gr-qc/9907019 [gr-qc]

1999 arXiv
[24]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, Journal of Optics13, 055107 (2011), arXiv:1101.0044 [physics.optics]

2011 arXiv
[25]

M¨ uller and D

T. M¨ uller and D. Weiskopf, General Relativity and Grav- itation44, 509 (2012), arXiv:1107.5650 [gr-qc]

2012 arXiv
[26]

W. A. Watters, A. Loeb, F. Laukien, R. Cloete, A. Delacroix, S. Dobroshinsky, B. Horvath, E. Kel- derman, S. Little, E. Masson, A. Mead, M. Ran- dall, F. Schultz, M. Szenher, F. Vervelidou, A. White, A. Ahlstr¨ om, C. Cleland, S. Dockal, N. Donahue, M. Elowitz, C. Ezell, A. Ge...

2023 arXiv
[27]

K. H. Knuth, P. Ailleris, H. A. Agrama, E. Ansbro, P. A. Budinger, T. Cai, T. Canuti, M. C. Cifone, W. B. Cornet, F. Courtade, R. Dolan, L. Domine, L. Dini, B. Friscourt, R. Graves, R. F. Haines, R. Hoff- man, H. Kayal, S. Little, G. P. Nolan, R. Pow- ell, M. Rodeghier, E. Rus...

2025
[28]

A. Loeb, A Warp Drive Could Shine Brighter than the Sun in the Earth’s Atmosphere, https://avi- loeb.medium.com/a-warp-drive-could-shine-brighter- than-the-sun-in-the-earths-atmosphere-11ac7c6e3a6e (2026)

2026
[29]

Servignat, J

G. Servignat, J. Novak, and I. Cordero-Carri´ on, Classical and Quantum Gravity40, 105002 (2023)

2023
[30]

Takahashiet al.(Particle Data Group), Int

F. Takahashiet al.(Particle Data Group), Int. J. Mod. Phys. A41, 2630011 (2026)

2026
[31]

Alcubierre, Classical and Quantum Gravity11, L73 (1994), arXiv:gr-qc/0009013 [gr-qc]

M. Alcubierre, Classical and Quantum Gravity11, L73 (1994), arXiv:gr-qc/0009013 [gr-qc]

1994 arXiv
[32]

Lax and B

P. Lax and B. Wendroff, Communications on Pure and Applied Mathematics13, 217 (1960), https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.3160130205

1960 doi
[33]

J. M. Mart ´ ı and E. M¨ uller, Living Reviews in Relativity 2, 10.12942/lrr-1999-3 (1999)

1999 doi
[34]

J. M. Stone, K. Tomida, C. J. White, and K. G. Felker, The Astrophysical Journal Supplement Series249, 4 (2020)

2020
[35]

J. A. Font, Living Rev. Relativ.11, 7 (2008)

2008
[36]

A. H. Taub, Phys. Rev.74, 328 (1948)

1948
[37]

Mignone and J

A. Mignone and J. C. McKinney, Monthly No- tices of the Royal Astronomical Society378, 1118 (2007), https://academic.oup.com/mnras/article- pdf/378/3/1118/18672055/mnras0378-1118.pdf

2007
[38]

W. G. Mathews, The Astrophysical Journal165, 147 (1971)

1971
[39]

W. I. Newman and N. D. Hamlin, SIAM Journal on Sci- entific Computing36, B661–B683 (2014)

2014
[40]

G. L. Bryan, M. L. Norman, B. W. O’Shea, T. Abel, J. H. Wise, M. J. Turk, D. R. Reynolds, D. C. Collins, P. Wang, S. W. Skillman, B. Smith, R. P. Harkness, J. Bordner, J.-h. Kim, M. Kuhlen, H. Xu, N. Goldbaum, C. Hummels, A. G. Kritsuk, E. Tasker, S. Skory, C. M. Simpson, O. H...

2014
[41]

L¨ ohner, Computer Methods in Applied Mechanics and Engineering61, 323–338 (1987)

R. L¨ ohner, Computer Methods in Applied Mechanics and Engineering61, 323–338 (1987)

1987
[42]

S. L. Shapiro, A. P. Lightman, and D. M. Eardley, The Astrophysical Journal204, 187 (1976)

1976
[43]

E. S. Weibel, Physical Review Letters2, 83–84 (1959)

1959
[44]

Crumley, D

P. Crumley, D. Caprioli, S. Markoff, and A. Spitkovsky, Monthly Notices of the Royal Astronomical Society485, 5105 (2019), quasi-parallel fiducial (γ 0 = 1.5,v≈ 0.75c,M A ≈M s ≈15,σ 0 = 0.007): downstream Te ≈0.23–0.3T i; quasi-perpendicular run:T p ≈6T e, 16 arXiv:1809.10809 ...

2019 arXiv
[45]

A. Spitkovsky, The Astrophysical Journal673, L39 (2008), unmagnetized relativistic e-ion Weibel-mediated shock: postshock near-equipartition,T e reaching 50% of Ti (abstract), arXiv:0706.3126 [astro-ph]

2008 arXiv
[46]

Vanthieghem, M

A. Vanthieghem, M. Lemoine, and L. Gremillet, The As- trophysical Journal Letters930, L8 (2022), unmagne- tized relativistic e-ion Weibel-mediated shocks (γ ∞ = 10–100): electrons heated up toT e ≃0.5T i downstream (quasi-equipartition) via coherent charge-separation field + J...

2022 arXiv
[47]

G. B. Rybicki and A. P. Lightman,Radiative Processes in Astrophysics(Wiley, 1985)

1985
[48]

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, Journal of Atmospheric and Oceanic Technology 16, 1854–1861 (1999)

1999
[49]

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon cross sections database (2010)

2010
[50]

M. Ave, M. Bohacova, B. Buonomo, N. Busca, L. Ca- zon, S. Chemerisov, M. Conde, R. Crowell, P. Di Carlo, C. Di Giulio, M. Doubrava, A. Esposito, P. Facal, F. Franchini, J. H¨ orandel, M. Hrabovsky, M. Iarlori, T. Kasprzyk, B. Keilhauer, H. Klages, M. Kleifges, S. Kuhlmann, G. ...

2008
[51]

Van Den Broeck, Classical and Quantum Gravity16, 3973 (1999), arXiv:gr-qc/9905084 [gr-qc]

C. Van Den Broeck, Classical and Quantum Gravity16, 3973 (1999), arXiv:gr-qc/9905084 [gr-qc]

1999 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Precisely,C A|v1→0 = 2.7 andC A|v1→1 = 3 2

By simply computing the two limitsv 1 →0 andv 1 →1, one finds thatC A is bounded from below and above by anO(1) constant. Precisely,C A|v1→0 = 2.7 andC A|v1→1 = 3 2 . Thus,δbehaves like∼ 1 M2 with an order 1 coefficient. This cold-limit/high Mach-number equivalence also holds for the other fluid quantities. This implies that large Mach numbers correspond ...

work page

[2] [2]

To high accuracy, most of the thermodynamic quantities are just algebra or cal- culus on the primitives through the EoS

Optical Depth A large amount of the science does not need explicit evolution during the simulation. To high accuracy, most of the thermodynamic quantities are just algebra or cal- culus on the primitives through the EoS. One of the most 6 important ones is the optical depth of the fluid. For the discretized grid, the Thomson optical depth is τT =σ T X xi≥...

work page

[3] [3]

Interaction Timescale The second defining quantity that determines whether the derived quantities can be computed in post- processing is the relation between the interaction timescale of the fluid constituents relative to the flow timescale. The ratio of the interaction timescale to the flow timescale is tei tf low = r π 2 mi me (Θe + Θi)3/2vs Zln Λ(n eσT...

work page

[4] [4]

Whether the pairs stay as tracer objects or cascade into an optically-thick fireball is the single qualitative question about the interaction’s appearance

Pair Production The post-shock energy budget exceeds the pair thresh- old by two orders of magnitude, so electron-positron pairs inevitably form. Whether the pairs stay as tracer objects or cascade into an optically-thick fireball is the single qualitative question about the interaction’s appearance. Thermal pair production switches on when the Wien tail ...

work page

[5] [5]

Luminosity Free-free emission from the hot electrons has a frequency-dependent emissivity. For a non-relativistic Maxwellian, the power per unit volume is dE dtdV = 2πkBTe 3me 1/2 25πe6 3hpmec3 ¯gB X s Z 2 s nsne (42) where ¯gB is the frequency average of the velocity aver- aged Gaunt factor,m e is the electron mass,h p is the planck constant, and whereEi...

work page

[6] [6]

The Code The deployed code heavily utilizes Athena++, an adaptive mesh refinement-based code for magnetohydro- dynamical simulations in special and general relativ- ity [28]. It fits well for this problem, since the back- ground spacetime is non-linear, stationary, and the only dynamical object is the relativistic unmagnetized fluid interacting with the c...

work page

[7] [7]

E. W. Lentz, Classical and Quantum Gravity38, 075015 (2021), arXiv:2006.07125 [gr-qc]

arXiv 2021

[8] [8]

Bobrick and G

A. Bobrick and G. Martire, Classical and Quantum Grav- ity38, 105009 (2021)

work page 2021