Structure Scalars and Gravitational Complexity in Anisotropic Configurations: Insights from Gauss-Bonnet Corrections

We assess the complexity of the charged anisotropic static cylindrical geometry in the framework of [Formula: see text] gravity, where [Formula: see text] represents the Gauss-Bonnet term. In order to comprehend the internal structure and stability of relativistic astrophysical systems under higher-curvature corrections, we compute modified field equations, the [Formula: see text] energy formula, the Tolman-Oppenheimer-Volkoff equation and the Einstein Maxwell field equations. Furthermore, we use the orthogonal decomposition of the Riemann tensor to compute the Weyl tensor components and derive several structural scalars, which offer valuable insights into the geometrical and physical properties of the system. One of these scalars, the term [Formula: see text] is referred to as the complexity factor, serving as a quantitative measure of the systems internal complexity arising from non-uniform energy density and anisotropy in the pressure distribution. By imposing the vanishing complexity condition, we obtain time-independent exact solutions corresponding to the Gokhroo-Mehra model, which describe physically viable compact configurations. This research shows that higher-order curvature contributions successfully reduce the system’s overall complexity, providing novel perspectives on how modified gravity controls the internal structure of self-gravitating anisotropic sources.