Effects of CDTT model on the stability of spherical collapse in Palatini f(R) gravity

The objective of this paper is to study the stability of an adiabatic anisotropic collapsing sphere in the context of Palatini f(R) gravity. In this framework, we construct the collapse equation with the help of the contracted Bianchi identities of the effective as well as the usual energy-momentum tensor. The perturbation scheme is applied on the fluid variables which accordingly cause a perturbation on the Ricci scalar. We explore the instability ranges in the Newtonian and post-Newtonian regimes. It is concluded that the stability of the star is governed by adiabatic index Γ1, which depends on the energy density profile, anisotropic pressure and dark source terms of the chosen f(R) model. We also explore our results when f(R)→R.