Construction of the pseudo Riemannian geometry on the base of the Berwald-Moor geometry

Abstract

The space of the associative commutative hyper complex numbers, H_4, is a 4-dimensional metric Finsler space with the Berwald-Moor metric. It provides the possibility to construct the tensor fields on the base of the analytical functions of the H_4 variable and also in case when this analyticity is broken. Here we suggest a way to construct the metric tensor of a 4-dimensional pseudo Riemannian space (space-time) using as a base the 4-contravariant tensor of the tangent indicatrix equation of the Berwald-Moor space and the World function. The Berwald-Moor space appears to be closely related to the Minkowski space. The break of the analyticity of the World function leads to the non-trivial curving of the 4-dimensional space-time and, particularly, to the Newtonian potential in the non-relativistic limit.