Jeans analysis of self-gravitating systems in f(R)-gravity

TL;DR

This paper extends the classical Jeans analysis to self-gravitating systems within f(R)-gravity, revealing new unstable modes and providing a modified dispersion relation that could impact astrophysical system modeling.

Contribution

It introduces a generalized Jeans instability analysis in f(R)-gravity, deriving a new dispersion relation and identifying unstable modes absent in Newtonian gravity.

Findings

Unstable modes are present in f(R)-gravity not seen in Newtonian analysis.

Derived a generalized Jeans wave-number for f(R)-gravity.

Discussed implications for astrophysical systems under modified gravity.

Abstract

Dynamics and collapse of collisionless self-gravitating systems is described by the coupled collisionless Boltzmann and Poisson equations derived from $f(R)$-gravity in the weak field approximation. Specifically, we describe a system at equilibrium by a time-independent distribution function $f_0(x,v)$ and two potentials $\Phi_0(x)$ and $\Psi_0(x)$ solutions of the modified Poisson and collisionless Boltzmann equations. Considering a small perturbation from the equilibrium and linearizing the field equations, it can be obtained a dispersion relation. A dispersion equation is achieved for neutral dust-particle systems where a generalized Jeans wave-number is obtained. This analysis gives rise to unstable modes not present in the standard Jeans analysis (derived assuming Newtonian gravity as weak filed limit of $f(R)=R$). In this perspective, we discuss several self-gravitating astrophysical systems whose dynamics could be fully addressed in the framework of $f(R)$-gravity.