Observer-robust energy condition verification for warp drive spacetimes

Abstract

We present \texttt{warpax}, a JAX-based toolkit that certifies the energy condition structure of warp drive spacetimes for all observers, in a frame-independent way, from the eigenstructure of the mixed stress-energy tensor $T^a{}_b$. At a Hawking--Ellis Type~I point, an eigenvalue inequality decides each energy condition exactly and for every observer. A Type~IV point has no rest frame and violates all of them unconditionally. Because the eigenvalues are boost invariants and no Eulerian normal is ever constructed, the test is well defined at all warp speeds, including $v_s \ge 1$. Across the warp drive family, this yields a clean dichotomy through the luminal transition: the irrotational Rodal geometry is globally Type~I at every speed, while the Alcubierre, Natário, and Van~den~Broeck bubble walls are dominated by Type~IV regions. The split is controlled by the vorticity of the ADM shift, with the Type~IV imaginary eigenvalue growing linearly, $f=κω$, in a controlled limit. Single-frame analyses understate this structure. For the Rodal drive, the Eulerian frame misses about $72\%$ of the wall weak-energy violations seen by boosted observers, a statement made analytic by a closed-form worst observer. A boost-invariant exoticity ranking places the irrotational drive roughly seventy times below the bubble-wall drives, and the wall null-energy deficit follows a universal $-C v_s^2$ law that makes the Santiago--Schuster--Visser no-go result quantitative. A geodesic-integrated averaged null energy condition and a Ford--Roman comparison preserve the ordering: every drive violates, and the Rodal geometry is the mildest.