Eur. Phys. J. C (2017) 77: 715
https://doi.org/10.1140/epjc/s10052-017-5300-0

Regular Article - Theoretical Physics

Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity

¹ Department of Theoretical Physics and History of Science, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, 48940, Leioa, Spain
² Dipartimento di Fisica E.R. Caianiello, INFN Gruppo Collegato di Salerno, Universitá di Salerno, 84084, Fisciano, SA, Italy

^* e-mail: ivan.demartino@ehu.eus

Received: 24 September 2017
Accepted: 12 October 2017
Published online: 26 October 2017

Abstract

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 . 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 self-gravitating astrophysical systems can be fully addressed in the Eddington-inspired Born–Infeld gravity. The latter modifies the Jeans instability in high densities environments, while its effects become negligible in star formation regions.