Traversable wormholes in f(R,Lm) gravity with gravitational lensing and photon dynamics

We study static and spherically symmetric traversable wormhole solutions within the framework of [Formula: see text] gravity, considering anisotropic matter sources. We focus on the specific functional form [Formula: see text], in which [Formula: see text] is identified with the energy density of the matter distribution. By adopting a Morris–Thorne spacetime with a constant redshift function and a power-law shape function [Formula: see text] ([Formula: see text]), we analyze the geometrical properties, matter content, and energy conditions. Two distinct cases, namely [Formula: see text] and [Formula: see text], are examined in detail. We show that the flare-out condition and asymptotic flatness are satisfied in both models. The null energy condition is violated only in the radial direction near the throat, while remaining satisfied transversely. The amount of exotic matter, quantified through the volume integral, is finite and controlled by the parameter [Formula: see text]. Further, the embedding diagrams confirm the traversable wormhole geometry. Moreover, we analyze the gravitational lensing signatures of the wormhole geometry through the effective potential and the light deflection angle, thereby characterizing the photon dynamics in the vicinity of the throat. Finally, we conclude that [Formula: see text] gravity admits viable traversable wormhole solutions supported by anisotropic matter, with the parameters [Formula: see text] and [Formula: see text] offering control over the distribution of matter and the degree of energy-condition violation.

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