Jeans Instability from post-Newtonian Boltzmann equation

TL;DR

This paper investigates how post-Newtonian corrections affect Jeans instability, showing that the critical mass for gravitational collapse is reduced compared to classical Newtonian predictions.

Contribution

It introduces a post-Newtonian framework for analyzing Jeans instability using the Boltzmann and Poisson equations with Maxwell-Jüttner distribution.

Findings

Post-Newtonian corrections lower the Jeans mass.

The dispersion relation includes post-Newtonian effects.

Gravitational collapse occurs at smaller masses in the post-Newtonian regime.

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-J\"uttner 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.