On the boundary cost of source-consistent warp shells

Abstract

We study classical energy-condition admissibility for subluminal, positive-energy warp shells. For the constructions examined here, the energy-condition failures are localized at the smooth source--vacuum transition rather than in the bulk interior. We introduce two \emph{source-first} shell ans"atze whose metric potentials are obtained from the Einstein constraints for a prescribed matter model: a shift-free S-shell and a T-shell whose shift is derived from the momentum constraint. We assess them with a five-criterion standard comprising regularity, constraint satisfaction, an explicit matter model, frame-independent energy-condition margins, and global diagnostics; the standard responds to the source-consistency critique of Barzegar, Buchert, and Vigneron. Applied to eight constructions spanning the canonical warp-drive classes, none passes the full standard. An independent frame-independent verification of the Fuchs constant-velocity shell confirms interior energy-condition compliance (0 of 13 interior probes violate) but reveals Hawking--Ellis Type~IV violations in the smoothing tail beyond the nominal shell. A frame-independent scan over shell compactness and thickness (600 configurations) yields no admissible configuration in either source-first class. The same boundary deficit appears in the shift-free S-shell and persists in the static $v_0=0$ limit, which ties it to the transition geometry rather than to the shift. Along a representative off-axis null ray the null-energy line integral is nevertheless positive for every source-prescribed shell; this is an exploratory diagnostic rather than a proof of the averaged null energy condition, but it shows that the pointwise boundary failures need not appear in that integral.