Insights of traversable wormhole geometries under complexity factor and different equations of state in modified gravity

Abstract

The focus of this investigation is to check whether charged traversable wormholes exist in the realm of $f(R,L_m,T)$ gravity. Considering the Morris–Thorne spacetime, we develop the wormhole geometry and derive the gravitational equations representing anisotropic fluid setup. To fulfill the objective of this study, we further assume a couple of equations of state to determine some necessary parameters linked with the wormhole models. This leads us to see that this cosmic fluid might provide an interesting explanation for the phenomenon of wormhole geometries. By employing both equations of state, we deduce the shape functions and analyze their consistency by satisfying fundamental conditions. We observe that the resulting functions meet key criteria and link two regions of spacetime that converge to asymptotic flatness. Afterward, we examine their practicality by checking if they violate or comply with the null energy conditions. In addition to that, we study the gravitational mass, complexity factor, embedding diagrams, and the volume integral quantifier. The results of this investigation imply that the constructed wormhole solutions adhere to the essential criteria, permitting their existence in the modified gravity under the considered standard model.