Torsion-Mediated Unification in Y n Space:Einstein–Maxwell Field Equations and Geodesic Dynamics

We develop a geometric framework for unified field theory based on Formula: see text space, an Formula: see text-dimensional manifold endowed with both a metric tensor Formula: see text and a torsion tensor Formula: see text. Starting from a least-action principle, we derive the vacuum gravitational field equations that generalize Einstein’s equations to include torsion contributions. We demonstrate that free particles and light rays follow geodesics that depend explicitly on both metric and torsion, with the geodesic equation reducing to the standard form only when torsion vanishes. In spaces with flat metric, we show that Maxwell’s equations emerge naturally from the Bianchi identities when torsion is appropriately identified with the electromagnetic field tensor. Explicit examples in three-dimensional Formula: see text space illustrate how non-zero torsion induces helical geodesics even in flat space, providing a geometric interpretation of electromagnetic effects on particle motion. This work establishes a consistent geometric framework that treats both metric and torsion as fundamental entities, offering a pathway toward the unification of gravitational and electromagnetic phenomena.