Field-theoretic construction of complexity-free anisotropic stars via extended decoupling

Modified theories of gravity have offered compelling alternatives for addressing the stability and structural features of self-gravitating systems. In this work, we explore the dynamics of anisotropic compact objects within the framework of $f(R,T,Q)$ gravity using an extended gravitational decoupling approach. Starting with a spherically symmetric anisotropic seed solution, we incorporate an additional gravitational source and formulate the corresponding field and conservation equations under strong matter-geometry coupling. The analytical structure is developed by imposing matching and Kuchowicz conditions to determine the unknown metric functions. Furthermore, we introduce a complexity-free condition along with an isotropized constraint to analyze the influence of coupling effects on the physical viability and stability of the system. Our results indicate that the matter-curvature interaction significantly enhances the stable configurations and reduces the overall complexity of the system. The impact of the decoupling parameter is also studied to illustrate the sensitivity of physical parameters, supported through graphical analysis. These findings provide deeper insight into the role of extended gravity and anisotropic effects in the formation and evolution of compact stellar objects.