Geodesic Deviation Equation In $f(Q)$-Gravity

Abstract

In the present paper we study the Geodesic Deviation Equation (GDE) in the modified $f(Q)$-gravity theories. The formulation of GDE in General Relativity in the case of the homogeneous and isotropic Friedman-Lemaître-Robertson-Walker (FLRW) spacetime is briefly discussed and then extended in modified $f(Q)$-gravity using its covariant counterpart. The generalised Mattig relation is obtained. Finally, an equivalent expression to the Dyer-Roeder equation in General Relativity in the case of $f(Q)$-gravity is presented.

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