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

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.