Linearized dispersion relations in viscous relativistic hydrodynamics

We compute the dispersion relations for scalar, vector and tensor modes of a viscous relativistic fluid, linearized around an equilibrium solution, divergence type theory (which, in theory, includes Israel-Stewart anisotropic hydrodynamics as particular cases) contrast them to corresponding results derived from kinetic under relaxation time approximation, causal first order theories. conclude that all approaches give similar dynamics scalar modes, while presented here also contains propagating damped waves, agreement with theory. Nonhydrodynamic are feature holographic fluids. These support application problems involving interaction between fluids gravitational waves.