Some observable physical properties of Finslerian Hayward-like black hole with global monopole charge and quintessence field

In this work, we investigate the geodesic motion of both massless and massive test particles in the vicinity of a spherically symmetric Finslerian Hayward-like black hole (FHBH) that is coupled to a quintessence field (QF) and carries a global monopole (GM). By examining the combined effects of the GM and QF, we observe significant deviations in the geodesic structure for both null and time-like particles when compared to the conventional BH models. Additionally, we explore spin-0 scalar field perturbations by solving the massless Klein–Gordon equation in this modified BH space-time background and analyze the influence of the Finslerian geometry, GM, and QF on the resulting scalar perturbative potential. Using the effective potential derived from null geodesics, we compute the transmission and reflection coefficients and discuss their physical implications. Furthermore, we numerically calculate the quasinormal modes (QNMs) frequencies based on the scalar perturbations potential and assess how the Finslerian modifications, along with the presence of GM and QF, affect the QNM spectrum.