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In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors. We will examine the dynamical analysis of geodesics which provides the derivation of the energy and the angular momentum of a particle moving along a geodesic of SFR spacetime. This study allows us to compare our model with the corresponding of general relativity (GR). In addition, the effective potential of SFR model is examined and it is compared with the effective potential of GR. The phase portraits generated by these effective potentials are also compared. Finally, we deal with the derivation of the deflection angle of the SFR spacetime and we find that there is a small perturbation from the deflection angle of GR. It comes from the anisotropic metric structure of the model and especially from a Randers term which provides a small deviation from GR.
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Kapsabelis, E.; Kevrekidis, Panayotis G.; Stavrinos, P. C.; and Triantafyllopoulos, A., "Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle" (2022). arXiv Preprint. 1340.