Finite Euclidean Mapping Framework (FEMF) - A Finite Euclidean Representation of General Relativity
Aviad Shetrit · Zenodo (CERN European Organization for Nuclear Research) · 2026
We propose an alternative geometric perspective on the dark matter problem. Rather than introducing additional unseen mass, we consider the possibility that the observed discrepancies in galactic rotation curves arise from the mapping between different geometric descriptions of space. We examine the translation between a Riemannian spacetime framework and an effective Euclidean representation used in the analysis of galactic dynamics. We argue that such a mapping requires, in general, the introduction of a finite boundary scale in order to remain mathematically well-defined. Using the SPARC database, we implement this Finite Euclidean Mapping Framework (FEMF) and apply it to a large sample of galaxies. The results demonstrate that the model successfully reproduces galactic rotation curves across a wide range of systems without the necessity for dark matter. Furthermore, a consistent and robust scaling relation emerges between the boundary scale and the galactic radius (R(B) ≈ 1.5 R(gal), with a correlation coefficient of r=0.94). These findings suggest that the observed missing mass discrepancy may be a direct consequence of geometric mapping rather than undetected physical matter.