On the linear stability of polytropic fluid spheres in $R^2$ gravity

TL;DR

This paper investigates the linear stability of polytropic fluid spheres in $R^2$ gravity, showing that the stability transition occurs at the maximum mass-central density point, similar to general relativity.

Contribution

It provides the first analysis of stability for polytropic spheres in $R^2$ gravity within the Jordan frame, extending stability criteria beyond general relativity.

Findings

Stability transition occurs at maximum mass-central density curve

Results align with general relativity stability criteria

Supports the applicability of classical stability analysis in $R^2$ gravity

Abstract

Within $R^2$ gravity, we study the linear stability of strongly gravitating spherically symmetric configurations supported by a polytropic fluid. All calculations are carried out in the Jordan frame. It is demonstrated that, as in general relativity, the transition from stable to unstable systems occurs at the maximum of the curve mass-central density of the fluid.