This paper investigates self-gravitating spherically symmetric fluid models in Brans-Dicke gravity by incorporating structure scalars. We obtain ten scalar quantities using orthogonal splitting of the Reimann tensor and write down the set of governing equations in terms of these scalars. We determine inhomogeneity factors and conclude that inhomogeneity is a necessary condition for the resultant fluid models. Finally, we explore static inhomogeneous anisotropic spherical solutions with the help of these structure scalars.

This paper discusses the phenomenon of evolving spherically symmetric cluster of stars in the presence of an exotic matter. To discuss evolutionary mechanism, we use the Starobinsky model of f(R) gravity as exotic matter and the structure scalars as evolutional parameters. We study various evolution modes such as isotropic pressure, quasi-homologous evolution, density homogeneity, and geodesic nature. The stability of homogeneous density of baryonic and non-baryonic matter is discussed using dissipation, tidal forces, anisotropic pressures, expansion and shear-effects. It is observed that the dark matter has remarkable impact on the evolutionary changes. Also, it is shown that the dissipation factor produces density inhomogeneity in expanding clusters with shear effects. We observe that high curvature geometry enhances quasi-homologous evolution in the presence of shear. We use star Her X-1 as test star to discuss physical behavior of Starobinsky model. It is found that the density of dark matter overcomes the density of matter for large values of dark matter parameter n.

In this article, we discuss several compact objects (GW 190814, PSR J0952-0607, PSR J0030+0451, PSR J0740+6620, GW 170817, PSR J1614-2230, PSR J2215+5135, and 4U 1608-52) to predict their masses and radii. A generalized polytropic stellar model within the framework of general relativity is derived by employing the Buchdahl-I metric. All the physical quantities such as energy density, radial, and tangential pressure are well behaved, continuous and no singularity is observed. The obtained results are compatible with observational data for compact objects under consideration. The physical stability of this model is determined by using generalized hydrostatic equilibrium condition, energy conditions, causality conditions and Herrera’s cracking technique. We observe that our model fulfills all of the requirements for being a physically realistic model.