A Lagrangian Formulation for Gravitational-Inertial Mass Decoupling in Exotic Vacuum Geometries

The equivalence principlethe identity of gravitational and inertial massis a cornerstone of general relativity. We present a Lagrangian eld theory in which this identity is broken by construction. We make four contributions. (i) We introduce a scalar eld Φ with simultaneous non-minimal curvature coupling (ξRΦ 2) and derivative coupling to the Einstein tensor (α G µν ∂ µ Φ ∂ ν Φ), and show that the resulting eective gravitational mass m g and inertial mass m i decouple for ξ > ξ c , with the mass ratio η = m g /m i passing through zero and becoming negative. (ii) We embed this eld in an EinsteinCartan spacetime with propagating torsion, demonstrating that torsion sourced by the decoupling eld produces spacetime eects that bend geodesics without generating Riemannian curvature singularities. (iii) We derive the modied Raychaudhuri equation in the presence of the decoupling eld and prove a singularity exclusion theorem: for ξ > ξ c , the eective null energy condition is violated, preventing geodesic focusing and excluding singularity formation. (iv) We propose a physical realization in the form of an Inertial-Neutral Containment Material (INCM)a nested cylindrical Casimir vacuum geometry with opposed zero-point eld gradientsand derive the stress-energy tensor for this conguration, establishing the conditions under which gravitational-inertial decoupling is energetically stable. The formalism extends the foundational work of Bondi (1957) on negative mass, connects to the EinsteinCartanSciamaKibble torsion framework, and provides the rst Lagrangian formulation unifying mass decoupling, torsion stabilization, and singularity exclusion within a single eld-theoretic framework.