Weak Gravitational Field in Finsler-Randers Space and Raychaudhuri Equation

TL;DR

This paper explores the weak gravitational field in Finsler-Randers space, deriving related equations of motion, geodesic deviation, and Raychaudhuri equation, with applications to gravitational waves and conditions for Einstein equations.

Contribution

It introduces a linearized Finsler-Randers framework, deriving generalized gravitational equations and curvature conditions, extending classical relativity concepts to Finsler geometry.

Findings

Derived generalized Raychaudhuri equation in Finsler-Randers space.

Established conditions for Einstein equations with electromagnetic fields.

Applied weak field analysis to gravitational wave scenarios.

Abstract

The linearized form of the metric of a Finsler - Randers space is studied in relation to the equations of motion, the deviation of geodesics and the generalized Raychaudhuri equation are given for a weak gravitational field. This equation is also derived in the framework of a tangent bundle. By using Cartan or Berwald-like connections we get some types "gravito - electromagnetic" curvature. In addition we investigate the conditions under which a definite Lagrangian in a Randers space leads to Einstein field equations under the presence of electromagnetic field. Finally, some applications of the weak field in a generalized Finsler spacetime for gravitational waves are given.