Geodesics Analysis, Perturbations and Deflection Angle of Photon Ray in Finslerian Bardeen-Like Black Hole with a GM Surrounded by a Quintessence Field

Abstract

In this study, the geodesic motion of both massless and massive test particles is examined around a spherically symmetric Finslerian Bardeen-like black hole (BH) that incorporates the effects of a quintessence field (QF) and a global monopole (GM). It is analyzed that how the presence of the QF and GM modifies the non-Riemannian spacetime geometry and significantly alters the dynamics of test particles compared to those in standard BH models, including numerical solutions for photon deflection trajectories. In addition, spin-0 scalar field perturbations is investigated by deriving a wave-like equation in the background of this modified BH geometry. It is studied that how the Finslerian structure, along with the QF and GM, influences the effective scalar perturbation potential. Using this potential, the spectrum of quasinormal modes (QNMs) are computed and the dynamical stability of the BH under scalar perturbations is assessed. Furthermore, the deflection of light rays is analyzed in the vicinity of the BH in the weak-field limit. These results show how the inclusion of Finslerian geometry, the QF, and the GM modifies the deflection angle compared to that in the classical Bardeen BH model formulated in Riemannian geometry. Overall, these findings highlight the significant role that non-Riemannian geometry, coupled with quintessential fields and global monopoles, plays in shaping the macroscopic and observational features of BHs.