https://doi.org/10.1140/epjc/s10052-022-11081-7
Regular Article - Theoretical Physics
Schwarzschild–Finsler–Randers spacetime: geodesics, dynamical analysis and deflection angle
1
Section of Astrophysics, Astronomy and Mechanics, Department of Physics, National and Kapodistrian University of Athens, 15784, Panepistimiopolis, Athens, Greece
2
Department of Mathematics and Statistics, University of Massachusetts, 01003-9305, Amherst, MA, USA
3
Department of Mathematics, National and Kapodistrian University of Athens, 15784, Panepistimiopolis, Athens, Greece
Received:
15
August
2022
Accepted:
25
November
2022
Published online:
6
December
2022
In this work, we extend the study of Schwarzschi ld–Finsler–Randers (SFR) spacetime previously investigated by a subset of the present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis et al. in Eur Phys J C 81(11):990, 2021). 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. We also derive an interesting relation between the deflection angles of the SFR model and the corresponding result in the work of Shapiro et al. (Phys Rev Lett 92(12):121101, 2004). These small differences are attributed to the anisotropic metric structure of the model and especially to a Randers term which provides a small deviation from GR.
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