Local stability of self-gravitating disks in $f(R)$ gravity

TL;DR

This paper derives a dispersion relation and new stability criteria for self-gravitating disks in $f(R)$ gravity, enhancing understanding of their stability properties under modified gravity theories.

Contribution

It introduces a dispersion relation and Toomre-like stability criteria specifically for disks in $f(R)$ gravity, extending classical results to modified gravity frameworks.

Findings

Derived dispersion relation for spiral density waves in $f(R)$ gravity

Established new Toomre-like stability criteria for disks

Analyzed stability conditions for fluid and stellar disks

Abstract

In the framework of metric $f(R)$ gravity, we find the dispersion relation for the propagation of tightly wound spiral density waves in the surface of rotating, self-gravitating disks. Also, new Toomre-like stability criteria for differentially rotating disks has been derived for both fluid and stellar disks.