On the role of dissipation in structure formation for dilute relativistic gases: the fluctuating static background case

Abstract

A correction to the Jeans stability criterion due to dissipation is established for the case of dilute high temperature gases. This effect is only relevant in the relativistic scenario and includes additional terms due to a density gradient driven heat flux, a non-vanishing bulk viscosity and the space-time dependent gravitational potential first order fluctuations. The result is obtained by thoroughly analyzing the exponentially growing modes present in the dynamics of density fluctuations in the linearized relativistic Navier–Stokes regime. The corrections to the corresponding Jeans mass and wavenumber are explicitly obtained and are compared to the non-relativistic and non-dissipative values using the transport coefficients obtained in the BGK approximation.