Effects of f(R) Model on the Dynamical Instability of Expansionfree Gravitational Collapse

TL;DR

This paper investigates how a specific f(R) gravity model influences the dynamical instability of expansionfree gravitational collapse with a central vacuum cavity, highlighting the roles of density, pressure anisotropy, and curvature corrections.

Contribution

It analyzes the impact of a chosen f(R) model on the instability conditions of expansionfree collapse, incorporating higher order curvature effects and perturbation analysis.

Findings

Instability range is independent of adiabatic index  but depends on density and pressure profiles.

Higher order curvature corrections influence the instability conditions.

The study extends understanding of gravitational collapse in modified gravity theories.

Abstract

Dark energy models based on f(R) theory have been extensively studied in literature to realize the late time acceleration. In this paper, we have chosen a viable f(R) model and discussed its effects on the dynamical instability of expansionfree fluid evolution generating a central vacuum cavity. For this purpose, contracted Bianchi identities are obtained for both the usual matter as well as dark source. The term dark source is named to the higher order curvature corrections arising from f(R) gravity. The perturbation scheme is applied and different terms belonging to Newtonian and post Newtonian regimes are identified. It is found that instability range of expansionfree fluid on external boundary as well as on internal vacuum cavity is independent of adiabatic index $\Gamma$ but depends upon the density profile, pressure anisotropy and f(R) model.