This paper investigates some physical features that give rise to complexity within the self-gravitating static cylindrical structure coupled with anisotropic distribution in the energy-momentum squared gravity. To accomplish this, we formulate the modified field equations and explore the structure of the astronomical body. The C-energy and Tolman mass are also calculated to discuss the matter distribution. We then obtain some structure scalars via orthogonal splitting of the Riemann tensor. Since, the complexity of the considered structure is influenced by a variety of variables, including anisotropic pressure and inhomogeneous energy density, etc. thus, we adopt the factor Y T F as the complexity factor. Further, the complexity-free condition along with the Gokhroo-Mehra model and polytropic equation of state are taken to generate their corresponding solutions. We deduce that the inclusion of additional terms of this modified theory leads to a more complicated system.

This paper investigates the complexity of a charged static sphere filled with anisotropic matter in the background of energy-momentum squared gravity. For this purpose, we evaluate the modified field and conservation equations to determine the structure of celestial system. The mass function is calculated through Misner-Sharp as well as Tolman mass definitions. The complexity of a self-gravitating system depends on different factors such as anisotropic pressure, electromagnetic field, energy density inhomogeneity, etc. We formulate the structure scalars by the orthogonal decomposition of the Riemann tensor to develop a complexity factor containing all vital features of the stellar structure. The vanishing complexity condition is achieved by setting the complexity factor equal to zero. Finally, we construct two static solutions by utilizing the energy density of Gokhroo-Mehra solution as well as the polytropic equation of state along with the zero complexity condition. It is found that electromagnetic field decreases the complexity of stellar structure.