The influence of density models on wormhole formation in Finsler–Barthel–Randers geometry

Abstract

Abstract This paper investigates the structure and stability of wormholes within the framework of Finsler–Barthel–Randers geometry, focusing on the influence of different density models. Finsler geometry, as a generalization of Riemannian geometry, allows for the incorporation of anisotropic characteristics, making it a valuable tool in exploring cosmological phenomena. By employing osculating Riemannian space approaches, we develop wormhole models under non-commutative geometry and power-law energy density distributions. We analyze the role of the Finsler parameter $$\eta $$ η while evaluating the energy conditions in each model. The specific models developed here with Finsler geometry offer insights into the physical viability of wormholes in this context, potentially resolving some of the longstanding issues in wormhole theory. These findings suggest that Finsler geometry, combined with osculating Barthel–Randers geometry, provides a promising avenue for the construction of stable and physically plausible wormhole structures, The results are validated through analytical solutions and 3-D visualizations, thus contributing to our broader understanding of gravitational physics and spacetime geometry.