Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable first order in the gradients formalism

TL;DR

This paper revisits structure formation in relativistic fluids using a kinetic theory-based heat flux relation, correcting previous Eckart-based results and deriving relativistic corrections to the Jeans wave number while maintaining stability.

Contribution

It introduces a new relativistic heat flux relation from kinetic theory that ensures stability and provides corrected relativistic Jeans criteria.

Findings

Relativistic corrections to the Jeans wave number are derived.

The new formalism maintains gravitational instability, unlike Eckart's framework.

The non-relativistic limit is correctly recovered in the new approach.

Abstract

The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart's framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature gradient term. It was shown that in such case, the pathological behavior of fluctuations leads to the disapperance of the gravitational instability responsible for structure formation. In the present work the problem is revisited now using a constitutive equation derived from relativistic kinetic theory. The new relation, in which the heat flux is not coupled to the hydrodynamic acceleration, leads to a consistent first order in the gradients formalism. In this case the gravitational instability remains, and only relativistic corrections to the Jeans wave number are obtained. In the calculation here shown the non-relativistc limit is recovered, opposite to what happens in Eckart's case.