Cosmological hydrodynamics with relativistic pressure and velocity

TL;DR

This paper derives cosmological hydrodynamic equations incorporating relativistic pressure and velocity within a weak gravity framework, emphasizing their potential significance in gravitational lensing phenomena.

Contribution

It provides a proper derivation of relativistic hydrodynamic equations in a cosmological setting, extending previous Minkowski background results.

Findings

Derived equations with relativistic pressure and velocity in cosmology.

Highlighted potential impact on gravitational lensing.

Clarified the derivation process for these equations.

Abstract

We present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. Previously we consistently derived special relativistic hydrodynamic equations with weak gravity in Minkowski background. With the relativistic pressure and velocity one cannot derive the cosmological counterpart by a simple transformation from equations in the Minkowski background. Here we present a proper derivation. We point out the potential importance of relativistic pressure and velocity in gravitational lensing.