Astrophysical signatures of traversable wormholes in modified gravity: Implications of different equations of state and complexity analysis

This paper outlines our findings of traversable wormhole solutions within the framework of modified $f(R,L_m,T)$ gravity. We define the Morris–Thorne spacetime in order to achieve our goal and derive the anisotropic gravitational equations for a particular linear model of the considered theory of gravity. Our investigation focuses on the potential of using certain equations of state to facilitate the presence of traversable wormholes. We thereby find that such cosmic fluid hints at a fascinating explanation for the emergence of wormhole geometries. Following this, we calculate the shape functions for two different redshift parameters and assess their viability by confirming that they violate the null energy conditions. Furthermore, we explore the active gravitational mass and the complexity factor for the derived solutions. It is noted that these quantities attain their lowest values close to the wormhole throat. Additionally, we investigate some other factors, specifically the volume integral quantifier and embedding diagrams. Our findings suggest that the established wormhole geometries comply with the required conditions, enabling their existence under this fluid-geometry coupling based gravity.