Generalized Relativity: A Unified Field Theory Based on Free Geodesic Connections in Finsler Space

An equation of structure on space-time is developed using the methods of Finslergeometry with an essentially unrestricted connection function, corresponding toa specification of the geodesic curves in the manifold. This contrasts with theusual approach in which the connection is derived in an explicit and restrictivemanner from a metric. The equation of structure based on the free geodesicconnection is found to incorporate, as a special case, equations which are closelycomparable to both Einstein's equation of gravity in the presence ofelectromagnetic energy and Maxwell's equations for a chargeless electromagneticfield. Beyond this unification of electromagnetism and gravity, the theory appearsto offer a wide scope for consideration of additional implications which mayprovide insights into other observed phenomena.