Geodesic Deviation Equation in $f (R,T)$ Gravity

TL;DR

This paper derives the modified geodesic deviation equation within $f(R,T)$ gravity, extending the mathematical framework and performing numerical analysis to understand its implications in cosmological models.

Contribution

It presents the first derivation of the GDE in $f(R,T)$ gravity and extends the Matting relation, providing new tools for analyzing modified gravity effects.

Findings

Derived the GDE in $f(R,T)$ gravity

Extended the Matting relation to this framework

Performed numerical analysis for null vectors

Abstract

In this paper, we investigate the modified Geodesic Deviation Equation (GDE) in the framework of $f(R,T)$ theory of gravity where $R$ and $T$ are the curvature scalar and the trace of the energy-momentum tensor, respectively, using the FLRW background. In this way, we obtain the GR equivalent (GDE) in $f(R,T)$ metric formalism. We also extend our work to the generalization of the Matting relation and perform the numerical analysis with GDE for null vector.