GEOMETRIZATION OF ELECTROMAGNETISM AND GRAVITY BASED ON A FINSLER SPACE-TIME WITH GAUGE-SYMMETRY

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 x(i) and velocity +(i):G(ij)(x, x) = (1 - bA(k)(X)x(k)/a)2. .g(ij)(x), where a = (-g(ij)(x)x(i)x(j))1/2 and b = e/mc2. Furthermore, all <<classical>> field equations of electro-gravity can be derived from an invariant action function involving the curvature tensor, C(h)ijk = fdelta(h)(i)F(jk) + H(h)ijk, 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 eta(ij).