Layered Gravity I: Foundational Theory and Metric Construction

Layered Gravity (LG) is proposed as a minimal and observationally testable extension of General Relativity that introduces an exponentially decaying oscillatory correction to the gravitational potential while preserving the second‑order structure of Einstein’s equations. We propose a minimal and observationally testable extension of General Relativity (GR), termed Layered Gravity (LG), in which an exponentially decaying oscillatory term is added to the gravitational potential. Unlike higher‑derivative, non‑local, or multi‑field modified gravity theories, LG preserves the second‑order structure of Einstein's equations, introduces no additional degrees of freedom, and remains fully local and ghost‑free by construction. Despite its simplicity, the oscillatory term generates nontrivial physical effects, including anisotropic effective pressures, sign‑changing effective energy density, and characteristic oscillatory deviations in the gravitational redshift profile. We derive the curvature tensors associated with the LG metric, interpret the resulting modifications as an effective energy‑momentum tensor, and perform numerical experiments using observational data from the isolated neutron star 1E 1207.4‑5209. The LG model predicts damped oscillatory deviations from the GR redshift curve, providing clear and quantitative criteria for falsification. These predictions distinguish LG from existing modified gravity frameworks and offer a novel approach to probing gravitational microstructure and its potential cosmological implications. LG therefore represents a minimal yet nontrivial extension of GR, combining mathematical simplicity with new observational signatures and a high degree of empirical testability.