  In this paper, we study the effects of polynomial $f(R)$ model on the
stability of homogeneous energy density in self-gravitating spherical stellar
object. For this purpose, we construct couple of evolution equations which
relate the Weyl tensor with matter parameters. We explore different factors
responsible for density inhomogeneities with non-dissipative dust, isotropic as
well as anisotropic fluids and dissipative dust cloud. We find that shear,
pressure, dissipative parameters and $f(R)$ terms affect the existence of
inhomogeneous energy density.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics