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

Summary

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 G_ij(x, x) depends on a particle’s position xⁱ and velocity xⁱ:G_ij(x, x) = (1 −bA_k(x)x^k/a)² g_ij(x), wherea = (- g_ij(x)xⁱx^j)^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, C_ijk ^h = fδ_i ^hF_jk + H_ijk ^h, 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 G_ij(x, x) in which g_ij(x) is replaced by constant η_ij.