Instability of Gravitating Object Under Expansion-free Condition in Rastall Theory

Abstract

In this paper, a perturbation scheme is applied to discuss the instability model of a gravitating source under expansion free condition upto Newtonian (N) and Post-Newtonian (pN) approximations in Rastall theory. For this purpose, we established field equations which are set of partial differential equations with the help of suitable metric and fluid. The linear perturbation scheme is used on these partial differential equations to formulate a collapse equation. We derived dynamical equations by applying N and pN approximations. These equations represent that instability of gravitating object is independent of adiabatic index Γ, while the instability of the gravitating object can be determined with the help of anisotropic pressure, energy density, Rastall parameter λ, and some constraints at N and pN approximations.