On the Theory of Gravitational Field in Finsler Spaces

Abstract

AbstractSome structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as gλχ(x, y) = γλχ(x) + hλχ(x, y) is proposed, where γλχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric hij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ȳi = K(x, y) yj in the internal field, is grasped by the Finslerian parallelism δyi (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δyχ = e(x) δyi. The whole metrical Finsler connection D for gλχ(i.e., Dgλχ = 0) is determined by taking account of the intrinsic behaviour δyχ.