Impact of Extended Starobinsky Model on Evolution of Anisotropic, Vorticity-free Axially Symmetric Sources

TL;DR

This paper investigates how an extended Starobinsky $f(R)$ gravity model affects the stability and collapse dynamics of anisotropic, vorticity-free axially symmetric gravitating bodies, highlighting the role of higher-order curvature corrections.

Contribution

It introduces a modified collapse equation in $f(R)$ gravity with an extended Starobinsky model for anisotropic sources, analyzing stability criteria in Newtonian and post-Newtonian regimes.

Findings

Supersymmetric supergravity $f(R)$ model effectively substitutes higher-order curvature corrections.

The stability range depends on the adiabatic index $\Gamma$ and differs between Newtonian and post-Newtonian eras.

Extended Starobinsky model influences the collapse dynamics and stability conditions of axially symmetric bodies.

Abstract

We study the implications of $R^n$ extension of Starobinsky model on dynamical instability of Vorticity-free axially symmetric gravitating body. The matter distribution is considered to be anisotropic for which modified field equations are formed in context of $f(R)$ gravity. In order to achieve the collapse equation, we make use of the dynamical equations, extracted from linearly perturbed contracted Bianchi identities. The collapse equation carries adiabatic index $\Gamma$ in terms of usual and dark source components, defining the range of stability/insatbility in Newtonian (N) and post-Newtonian (pN) eras. It is found that supersymmetric supergravity $f(R)$ model represents the more practical substitute of higher order curvature corrections.