Topologically dynamical complex objects and structure scalars

In this study, we explore topologically spherical relativistic objects and analyze the factors that are involved in maintaining the smooth composition of anisotropic content. The corresponding field equations resulting from this extension show a different behavior due to the higher-order correction terms. We study the role of structure scalar in the possible modeling of complex objects in a well-known way, discussed by [L. Herrera, A. Di Prisco and J. Ospino, Phys. Rev. D 98 (2018) 104059]. After orthogonally splitting the curvature tensor, the associated dynamical equations are evaluated. We examine the complexity of the pattern of evolution by considering the homologous constraint. Furthermore, in the presence and absence of dissipation, the behavior, characteristics, and stability of the self-gravitating structures are analyzed. It is inferred that correction terms are trying to disturb the usual scenario of the homologous evolution of the relativistic dynamical system.