Shear-free and homology conditions for self-gravitating dissipative fluids

TL;DR

This paper investigates shear-free conditions in dissipative relativistic fluids, revealing their connection to homology laws and implications for astrophysical models in the Newtonian limit.

Contribution

It demonstrates the equivalence of shear-free and homogeneous expansion conditions to homology laws in the Newtonian limit and explores deviations with astrophysical applications.

Findings

Shear-free condition implies linear homology law in Newtonian limit.

Shear-free and homogeneous expansion conditions are equivalent in the Newtonian limit.

Deviations from homology have potential astrophysical applications.

Abstract

The shear free condition is studied for dissipative relativistic self-gravitating fluids in the quasi-static approximation. It is shown that, in the Newtonian limit, such condition implies the linear homology law for the velocity of a fluid element, only if homology conditions are further imposed on the temperature and the emission rate. It is also shown that the shear-free plus the homogeneous expansion rate conditions are equivalent (in the Newtonian limit) to the homology conditions. Deviations from homology and their prospective applications to some astrophysical scenarios are discussed, and a model is worked out.