Schwarzschild–Finsler–Randers spacetime: geodesics, dynamical analysis and deflection angle

Abstract In this work, we extend the study of Schwarzschi ld–Finsler–Randers (SFR) spacetime previously investigated by a subset present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis 81(11):990, 2021). We will examine dynamical analysis geodesics which provides derivation energy and angular momentum particle moving along geodesic SFR spacetime. This allows us to compare our model with corresponding general relativity (GR). addition, effective potential is examined it compared GR. The phase portraits generated these potentials are also compared. Finally deal deflection angle find that there small perturbation from derive an interesting relation between angles result work Shapiro (Phys Rev Lett 92(12):121101, 2004). These differences attributed anisotropic metric structure especially Randers term deviation