A seven dimensional extension of General Relativity

This work develops a seven-dimensional (7D) extension of general relativity aimed at explaining galactic rotation curve anomalieswithout invoking dark matter. The formulation is based on a 7 × 7 metric with Lorentzian signature, preserving the covariance andinternal consistency of Einstein’s field equations. Within this framework, an effective fluid-like contribution emerges that modi-fies geodesic motion only on galactic and cosmological scales, while remaining negligible in the solar system. As a consequence,classical tests of general relativity, including GPS-based time dilation measurements, remain unaffected, in agreement with ex-perimental null results. By contrast, the cumulative corrections at large radii reproduce the observed flatness of rotation curves,thereby providing a natural explanation for phenomena traditionally attributed to dark matter halos. In addition to its astrophysi-cal implications, the theory suggests possible links to black hole dynamics, the large-scale structure of spacetime, and the energycontent of the vacuum, opening new perspectives on gravitational physics.