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

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.

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• An anisotropic version of Tolman VII solution in $f(R,T)$ gravity via Gravitational Decoupling MGD Approach
• Decoupling gravitational sources by MGD approach in Rastall gravity
• A periodic varying deceleration parameter in $f(R,T)$ gravity
• Phantom fluid supporting traversable wormholes in alternative gravity with extra material terms
• $f(R,T)$ models applied to Baryogenesis
• Late time cosmological approach in mimetic $f(R,T)$ gravity
• A conservative energy-momentum tensor in the $f(R,T)$ gravity and its implications for the phenomenology of neutron stars
• Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism
• Models of Collapsing and Expanding Anisotropic Gravitating Source in $f(R,T)$ Theory of Gravity
• Reconstruction of $f(R,T)$ gravity model via the Raychaudhuri equation
• Unimodular $f(G)$ gravity
• Geodesic deviation equation in generalized hybrid Metric-Palatini gravity