Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle

TL;DR

This paper analyzes the Schwarzschild-Finsler-Randers spacetime, focusing on geodesic dynamics, effective potentials, and light deflection, revealing small deviations from general relativity due to anisotropic metric effects.

Contribution

It extends previous work by deriving geodesic properties, effective potentials, and deflection angles in SFR spacetime, highlighting differences from GR caused by Randers metric terms.

Findings

Small perturbation in deflection angle compared to GR

Effective potential analysis shows differences from GR

Phase portraits illustrate dynamical distinctions

Abstract

In this work, we extend the study of Schwarzschild-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 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 the GR.