Linearized dispersion relations in viscous relativistic hydrodynamics

TL;DR

This paper compares dispersion relations in viscous relativistic hydrodynamics derived from different theoretical frameworks, finding consistent results for scalar and vector modes and identifying propagating tensor waves in a divergence type theory.

Contribution

It introduces a divergence type theory framework that includes Israel-Stewart and anisotropic hydrodynamics, and compares its dispersion relations with kinetic and causal first order theories.

Findings

Scalar and vector modes show similar dynamics across approaches

The divergence type theory predicts propagating damped tensor waves

Holographic fluids exhibit non hydrodynamic tensor modes

Abstract

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 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. Non hydrodynamic 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.