On Dynamical Instability of Kantowski-Sachs Space-Time in f(R) Theory of Gravitation

Abstract

In this paper, we have studied the instability regions of Kantowski-Sachs space-time in the framework of f(R) theory of gravitation.The dynamical equations are constructed with the help of contracted Bianchi identities. The perturbation approach is used for the stability analysis of the system under consideration. We have obtained the general collapse equation from the dynamical equations through perturbation scheme. This collapse equation with adiabatic index Γ₁ is used to study the instability regions in Newtonian (N) and Post-Newtonian (pN) regimes. We have concluded that the adiabatic index Γ₁ or stiffness parameter plays a key role to define the instability of the system which depends upon the physical parameters.