  We analyze the stability of self-gravitating systems which dynamics is
investigated using the collisionless Boltzmann equation, and the modified
Poisson equation of Eddington-inspired Born-Infield gravity. These equations
provide a description of the Jeans paradigm used to determine the critical
scale above which such systems collapse. At equilibrium, the systems are
described using the time-independent Maxwell- Boltzmann distribution function
$f_0(v)$. Considering small perturbations to this equilibrium state, we obtain
a modified dispersion relation, and we find a new characteristic scale length.
Our results indicate that the dynamics of the self-gravitating astrophysical
systems can be fully addressed in the Eddington-inspired Born-Infield gravity.
The latter modifies the Jeans instability in high densities environments while
its effects become negligible in the star formation regions.
