Observer-robust energy condition verification for warp drive spacetimes

Abstract

Abstract Energy-condition tests for warp-drive spacetimes must account for all admissible causal directions at each point. We use the classical S-lemma to express the null, weak and strong conditions as 4×4 linear matrix inequalities; the dominant condition requires two such tests. These criteria require neither Hawking–Ellis classification nor a rapidity cutoff. For the null condition in a fixed orthonormal tetrad, the optimized multiplier margin equals half the minimum normalized null-energy contraction. Interval evaluation of the metric and curvature provides pointwise certificates and global bounds on its minimum over the bubble wall. On flat unit-lapse slices, the momentum constraint relates Eulerian momentum to shift vorticity. For smooth shifts on all of Euclidean space with bounded vorticity, momentum vanishes identically precisely for a gradient plus rigid rotation. For shifts linear in speed, integrated negative Eulerian energy scales exactly quadratically when finite, with a fixed profile and integration domain on these slices. We implement the tests in warpax, a JAX toolkit, and compare four warp-drive geometries at matched parameters across subluminal and superluminal speeds. At the reference parameters, the global bounds establish null-energy violation in all four bubble walls. The ideal irrotational Rodal profile has zero Eulerian momentum and is everywhere Type I; Type-IV regions are detected in the other sampled walls. For Rodal, the Eulerian reading misses about 73% of the sampled wall weak-energy violations. These numerical type labels and sampled fractions are distinct from the interval bounds. Finite-segment null-geodesic integrals and flat-space quantum-inequality estimates supplement the pointwise analysis.