Light Deflection and Stable Thin‐Shell Wormhole Structures for ρ(R,R′) and ρ(R2,R′) Profiles in f(R,Lm) Gravity

ABSTRACT This paper investigates light deflection in wormhole spacetimes within the extended gravity model , where and are Ricci scalar and Lagrangian matter, respectively. Inspired by the density formulations proposed by Elizalde and Khurshudyan [ https://doi:10.1103/PhysRevD.99.024051 Phys. Rev. D 99 , no.2, 024051 (2019)], the profiles and are used to derive shape functions that meet the necessary conditions for wormhole traversability. The Tolman–Oppenheimer–Volkoff (TOV) equation maintains equilibrium through the hydrostatic and anisotropic balancing forces. The deflection angle highlights lensing transitions, the volume integral quantifier indicates minimal exotic matter, and the growth of the effective potential with angular momentum signals orbit stability. The linear perturbation approach identifies the stability region, demonstrating that the adopted configurations produce stable, traversable wormholes with realistic lensing.