Local fragmentation of thin disks in Eddington-inspired gravity

TL;DR

This paper derives a modified Toomre's stability criterion for thin disks within Eddington-inspired Born-Infeld gravity, revealing how the free parameter $$ influences disk stability and fragmentation.

Contribution

It introduces a generalized Toomre's criterion in EiBI gravity, showing how the parameter $$ affects the stability and fragmentation of rotating thin disks.

Findings

Negative  destabilizes disks.

Positive  stabilizes disks and suppresses fragmentation.

Only an annular region remains unstable, with width depending on .

Abstract

We find the generalized version of the Toomre's criterion for the stability of a rotating thin disk in the context of Eddington inspired Born-Infeld (EiBI) gravity which possesses one free parameter $\chi$. To do so we use the weak field limit of the theory and find the dispersion relation for the propagation of matter density waves on the surface of a self-gravitating and differentially rotating disk. Finally we find a new version of Toomre's stability criterion for thin disks. We show that EiBI gravity with negative $\chi$ destabilizes all the rotating thin disks. On the other hand EiBI with positive $\chi$ substantially can suppress the local fragmentation, and has stabilizing effects against axi-symmetric perturbations. More specifically, we show that only an annulus remains unstable on the surface of the disk. The width of the annulus directly depends on the magnitude of $\chi$.