Exploring the applicability of traversable wormhole formation in f(R,Lm)gravity

In this work, we construct three different models of static wormhole (WH) geometries within the realm of f(R,Lm)gravity theory. We start by deriving the corresponding field equations for the Morris–Thorne WH geometry in the context of anisotropic matter distribution under the generic form of f(R,Lm)gravity. By adequately specifying the key features of three different shape function models generated with different assumptions about their matter content, and assuming that WHs exert no tidal force by setting the gravitational redshift function to be a constant or φ′(r)=0, we disclose a variety of exact WH solutions in the theory. Our exact solutions for f(R,Lm)show that for all three classes of WHs found, the energy density is consistently positive in all spacetime, while the radial pressure is negative. This signifies that exotic matter is mandatory for the existence of WHs in f(R,Lm)gravity. We have also applied the energy conditions (ECs) for the WHs’ physical content and found that exact WH models are filled with exotic matter that violates the necessary ECs throughout spacetime and makes them compatible and traversable.