Investigating the influence of non-vanishing vector fields on wormhole stability in Finsler–Randers geometry

This study examines the physical and geometrical implications of the vector field [Formula: see text] within the Finsler–Randers metric framework, particularly in the context of Wormhole (WH) geometry. By introducing a non-vanishing vector field with a vanishing covariant derivative to the Finsler manifold via osculation, we derived new Finsler metrics specifically adapted for WH structures. This approach alters traditional geometric interpretations by incorporating direction-dependent variables ([Formula: see text]), which significantly influence the redshift and shape functions of WHs. The resulting differential equations reveal how these modifications impact the geometry and offer new insights into the stability and properties of WHs. In Case 1, both constant and dynamic redshift functions showed how the vector field affects gravitational redshift and energy conditions, crucial for WH stability and traversability, through the parameter [Formula: see text]. In Case 2, the focus was on the vector field impact on the WH geometry emphasizing its role in defining the spatial structure and throat. Additionally, we explored different models under constant and variable equation of state parameters, [Formula: see text], leading to new shape functions that highlight the unique characteristics of WHs in a Finslerian background.