Telleparallel Lagrange Geometry and a Unified Field Theory: Linearization of the Field Equations

TL;DR

This paper applies a linearization scheme to the field equations in a teleparallel Lagrange geometry-based unified field theory, leading to simplified geometric objects, a connection with GFT, and an approximate solution.

Contribution

It introduces a linearization approach to the field equations, revealing key geometric and physical insights in the context of a unified field theory.

Findings

Vertical geometric objects become independent of position after linearization

Linearized theory matches GFT in first-order approximation

An approximate solution to vertical field equations is derived

Abstract

The present paper is a natural continuation of our previous paper: "Teleparallel Lagrange geometry and a unified field theory, Class. Quantum Grav., 27 (2010), 045005 (29pp)" \cite{WNA}. In this paper, we apply a linearization scheme on the field equations obtained in \cite{WNA}. Three important results under the linearization assumption are accomplished. First, the vertical fundamental geometric objects of the EAP-space loose their dependence on the positional argument $x$. Secondly, our linearized theory in the Cartan-type case coincides with the GFT in the first order of approximation. Finally, an approximate solution of the vertical field equations is obtained.