Jeans instability from post-Newtonian Boltzmann equation

Abstract

Abstract Jeans instability within the framework of post-Newtonian Boltzmann and Poisson equations are analyzed. The components of the energy–momentum tensor are calculated from a post-Newtonian Maxwell-Jüttner distribution function. The perturbations of the distribution function and gravitational potentials from their background states with the representation of the perturbations as plane waves lead to a dispersion relation with post-Newtonian corrections. The influence of the post-Newtonian approximation on the Jeans mass is determined and it was shown that the mass necessary for an overdensity to begin the gravitational collapse in the post-Newtonian theory is smaller than the one in the Newtonian theory.