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

Automated summary

The dispersion relations for scalar, vector, and tensor modes of a viscous relativistic fluid were calculated and compared with results derived from kinetic theory and causal first-order theories. The study found that different methods show similar dynamics for scalar and vector modes, while the specific divergence-type theory presented contains propagating damped tensor waves. These conclusions support the application of hydrodynamics in problems involving the interaction between fluids and gravitational waves.