Dispersion relations of relativistic radiation hydrodynamics

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.