Gravity in Physically Meaningful Reference Frames: Effective Geometry, Harmonic Extraction, and Reference-Frame-Covariant Field Equations

Abstract We develop a reference-frame-covariant interpretation and formulation of gravitation on a physically meaningful background spacetime. The starting point is the strict distinction between a physical reference frame and a coordinate system. On this basis, inertial and non-inertial frames are assigned different but equally meaningful spacetime structures, and covariance is reformulated as covariance with respect to transformations between physically meaningful reference frames rather than arbitrary coordinate relabelings. Gravitation is interpreted as a real physical field acting on a background spacetime, while the generalized gravitational potential tensor is introduced as the primary effective variable and the associated Riemannian geometry is interpreted as an induced representation of the same field content. The de Donder conditions are reinterpreted as the principle of harmonic extraction: in an inertial reference frame with global Cartesian coordinates, they make explicit the flat-background field-theoretic content underlying the effective geometric description. The resulting framework clarifies the status of the field equations, conservation laws, and the physical interpretation of solutions. In particular, it gives a privileged status to the harmonic/Fock-type exterior solution, so that the present theory is not merely a reformulation at the level of language but may lead to observable deviations from the standard geometrical reading of the Schwarzschild family at higher weak-field orders. Status: Submitted manuscript.This is the author-created version submitted to Classical and Quantum Gravity. Access: The full manuscript is not publicly available in this record. Rights: Copyright remains with the author. Metadata, abstract, and scholarly citation are publicly available. No Creative Commons or other open-access reuse licence is granted for the manuscript file.