Dispersion relations of relativistic radiation hydrodynamics

TL;DR

This paper derives exact linear dispersion relations for shear, heat, and sound waves in relativistic matter-radiation fluids, providing insights into their stability, propagation, and damping characteristics.

Contribution

It presents a novel analytical computation of dispersion relations in relativistic radiation hydrodynamics, applicable across all wave numbers, enhancing understanding of fluid stability and wave behavior.

Findings

Accurate dispersion relations for shear, heat, and sound waves in relativistic fluids.

Insights into stability, propagation speeds, and damping of waves.

Analytic expressions valid for any wave number.

Abstract

We compute the linearised dispersion relations of shear waves, heat waves, and sound waves in relativistic ''matter+radiation'' fluids with grey absorption opacities. This is done by solving radiation hydrodynamics perturbatively in the ratio ''radiation stress-energy''/''matter stress-energy''. The resulting expressions $\omega \, {=} \, \omega(k)$ accurately describe the hydrodynamic evolution for any $k\, {\in}\, \mathbb{R}$. General features of the dynamics (e.g., covariant stability, propagation speeds, and damping of discontinuities) are argued directly from the analytic form of these dispersion relations.