Evolution of cluster of stars in f ( R ) gravity

This paper explores the dynamics of evolving cluster of stars in the presences of exotic matter. The $f\left(R\right)$ theory is used to presume exotic terms for evolution scenario. We use structure scalars as evolution parameters to explore dynamics of spherically symmetric distribution of evolving cluster of stars. We consider Starobinsky model, $f\left(R\right)=R+\epsilon R^2$ and study different evolution modes having features like isotropic pressure, density homogeneity, homologous and geodesic behavior. It is concluded that dynamics of these modes of evolution depends upon the behavior of dark matter. The presences of dark matter directly affects the features of cluster like anisotropic pressure, dissipation, expansion, shear as well as density homogeneity. The evolution having homogeneous density and isotropic pressure depends upon conformally flat and non-dissipative behavior of baryonic as well as non baryonic matter. The dissipation factor induces density inhomogeneity in the expanding clusters having shear effects. The non dissipative homologous evolution also be discussed in the presence and absence of shear effects. It is found that high curvature geometry in the presence of shear supports homologous evolution. Expanding clusters are also explored in the presences of dissipation of dark matter and shear effects. By using quasi-homologous conditions the geodesic evolution is studied. It is theoretically showed that geodesic and homologous conditions depends upon each other. Finally we investigate behavior of Starobinsky model for a stellar structure $4U1820-30$ toward center. It is found that for increasing values of $\epsilon$ the DM behavior is dominant as compare to baryonic matter.