Spin–Torsion Compensation in Alcubierre Warp-Drive Spacetimes within Einstein–Cartan Gravity
Abstract
We present a self-contained treatment of Alcubierre warp-drive spacetimes within Einstein–Cartan (EC) gravity in which the algebraic spin–torsion sector, sourced by a Weyssenhoff spin fluid, absorbs the exotic part of the required stress–energy. Working in the 3+1 (Eulerian) decomposition we derive the exact geometric energy density of the tanh-wall bubble, ρ̃_GR = −(v_s²/4c²)[(y²+z²)/r_s²](df/dr_s)², together with — for the first time in this setting — the exact Eulerian momentum density and wall stresses, all verified to machine precision against an Einstein tensor built from closed-form metric derivatives. The density inverts into the spin threshold s_min = v_sσ tanh²(2σR)/[2κc² tanh(σR)]; for baseline parameters (R = 10 m, σ = 100 m⁻¹, v_s = 0.5c), s_min ≈ 4.0×10³⁵ kg m⁻¹ s⁻¹, equivalent to ≈ 7.6×10⁶⁹ aligned ħ/2 carriers per cubic metre. Because the comoving spin fluid contributes no Eulerian momentum flux, the matter sector must carry the full geometric flux, which peaks at 6.16 times the density scale; a complete pointwise audit then shows that the weak, null, and strong energy conditions hold for all observers if and only if s ≥ 2.672 s_min, while the dominant energy condition is unattainable for any s — on the bubble axis the energy density vanishes identically while the transverse stress does not. We reframe energetics around quasi-local wall energy (≈ 7.8×10⁴⁶ J at threshold; ADM mass identically zero), resolve the parked-shell/black-hole tension via the…
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