On Weak Fields in Finsler Spaces

TL;DR

This paper explores weak and strong field approximations in Finsler spaces, deriving linear and non-linear field equations, and discusses unification of gravity and electromagnetism within a geometric framework.

Contribution

It introduces a new geometric approach to derive field equations in Finsler spaces, unifying gravitational and electromagnetic theories in both Riemannian and Berwald-Moor spaces.

Findings

Linear field equations in weak fields

Non-linear interactions in stronger fields

Unification of gravity and electromagnetism

Abstract

It is shown that in the weak field approximation the new geometrical approach can lead to the linear field equations for the several independent fields. For the stronger fields and in the second order approximation the field equations become non-linear, and the fields become dependent. This breaks the superposition principle for every separate field and produces the interaction between different fields.The unification of the gravitational and electromagnetic field theories is performed in frames of the geometrical approach in the pseudo Riemannian space and in the curved Berwald-Moor space.