On the Infeasibility of Low-Energy Warp Drive via Metamaterial Gravitational Coupling

Recent ``low-energy’’ warp-drive concepts propose replacing the constant gravitational coupling ${\kappa }_0$ with a spatially varying scalar field $\kappa (x)$ set by an engineered metamaterial’s electromagnetic response. We show that the idea fails on both theoretical and experimental grounds. A prescribed, non-dynamical $\kappa (x)$ in the field equation $G^{\mu \nu }=\kappa (x)T^{\mu \nu }$ clashes with the contracted Bianchi identity, ${\mathrm{\nabla }}_{\mu }{G}^{\mu \nu }\equiv 0$, forcing ${\mathrm{\nabla }}_{\mu }{T}^{\mu \nu }\mathrm{\ne }0$ and thus violating local energy-momentum conservation. Making $\kappa (x)$ dynamical yields a scalar-tensor theory in which the scalar mediates a new long-range force that breaks the strong equivalence principle; Solar-System and pulsar-timing experiments already restrict $\mathrm{\mid }\gamma -1\mathrm{\mid }\lesssim {10}^{-5}$, excluding any technologically useful coupling. Junction-condition analysis further shows that any interface where $\kappa$ changes demands a $\delta$-function layer of stress-energy, while even steep continuous profiles are ruled out by torsion-balance, lunar-laser, and spacecraft Doppler measurements. Hence the concept is untenable: a non-dynamical scheme violates conservation laws, and its scalar-tensor completion is falsified by existing data…