Jeans instability from post-Newtonian Boltzmann equation

Gilberto M Kremer

doi:10.1140/epjc/s10052-021-09728-y

Gilberto M Kremer

Open Access

https://doi.org/10.1140/epjc/s10052-021-09728-y

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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.

Highlights

The first attempt to describe instabilities of self-gravitating fluids from the hydrodynamic equations coupled with the Newtonian Poisson equation was due to Jeans [1]
In this work the Jeans instability was analysed within the framework of the Boltzmann and Poisson equations that follow from the first post-Newtonian theory
The components of the energy–momentum tensor in the Poisson equations were determined from the Maxwell–Jüttner distribution function

Summary

Introduction

The first attempt to describe instabilities of self-gravitating fluids from the hydrodynamic equations coupled with the Newtonian Poisson equation was due to Jeans [1] He determined from a dispersion relation a wavelength cutoff, nowadays known as Jeans wavelength, such that for small wavelengths than the Jeans wavelength the perturbations propagate as harmonic waves in time but for large wavelengths the perturbations will grow or decay with time. The collapse of a mass density inhomogeneity occurs whenever the inwards gravitational force is bigger than the outwards pressure force Another method to analyse the Jeans instability is to consider the collisionless Boltzmann equation coupled with the Newtonian Poisson equation The representation of the perturbations as plane waves results into a dispersion relation where the post-Newtonian influence in the Jeans mass is analyzed.

Boltzmann equation

Jeans instability

Summary