Geometrization of electromagnetism and gravity based on a finsler space-time with gauge symmetry-II

Abstract

The Finsler geometry is a more suitable framework for physics than the Riemannian geometry. Both electromagnetism and gravity can be geometrized such that the electrogravitational phenomena are consequences of a curved Finsler space-time with a local gauge symmetry. The fundamental metric tensor Gij(x, x) depends on a particle’s position xi and velocity xi:Gij(x, x) = (1 −bAk(x)xk/a)2 gij(x), wherea = (- gij(x)xixj)1/2 andb = e/mc2. Furthermore, all 〈classical〉 field equations of electro-gravity can be derived from an invariant action function involving the curvature tensor, Cijkh = fδihFjk+ Hijkh, of the Finsler space-time. The results of such a geometrization are consistent with experiments. They show that the usual concept of a flat space-time with an additional electromagnetic field is physically equivalent to that of a curved Finsler space-time with the metric tensor Gij(x, x) in which gij(x) is replaced by constant ηij.