Abstract In this article, we study further applications of the Schwarzschild–Finsler–Randers (SFR) model which was introduced in a previous work Triantafyllopoulos et al. (Eur Phys J C 80(12):1200, 2020). model, investigate curvatures and generalized Kretschmann invariant plays crucial role for singularities. addition, derived path equations are used gravitational redshift SFR-model these compa...