Generalized relativity: A unified field theory based on free geodesic connections in Finsler space

摘要

An equation of structure on space-time is developed using the methods of Finsler geometry with an essentially unrestricted connection function, corresponding to a specification of the geodesic curves in the manifold. This contrasts with the usual approach in which the connection is derived in an explicit and restrictive manner from a metric. The equation of structure based on the "free" geodesic connection is found to incorporate, as a special case, equations which are closely comparable to both Einstein's equation of gravity in the presence of electromagnetic energy and Maxwell's equations for a chargeless electromagnetic field. Beyond this unification of electromagnetism and gravity, the theory appears to offer a wide scope for consideration of additional implications which may provide insights into other observed phenomena. [References: 7]