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

Abstract: 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, $\nabla_\mu G^{\mu\nu} \equiv 0$, forcing $\nabla_\mu T^{\mu\nu} \neq 0$ 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 $|\gamma - 1| \lesssim 10^{-5}$, 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..