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 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.
Highlights
Recent developments in relativistic heavy ion collisions [1] and cosmology [2] have brought attention to the physics of relativistic viscous fluids [3,4], since the realization that hydrodynamical models act as an attractor to more complex physics even on short times scales [5,6,7,8,9,10,11]
Progress has been impaired by the fact that, unless the situation for nonrelativistic fluids described by the Navier-Stokes equations, no single approach to relativistic viscous fluids has achieved consensus status in the community
This is not a matter of “right” vs “wrong” but rather that different approaches best capture some aspects of the complex physics of relativistic fluids
Summary
Recent developments in relativistic heavy ion collisions [1] and cosmology [2] have brought attention to the physics of relativistic viscous fluids [3,4], since the realization that hydrodynamical models act as an attractor to more complex physics even on short times scales [5,6,7,8,9,10,11]. Dispersion relations are known from kinetic theory under the relaxation time approximation [1,21,22,23,24] They may be found from quantum field theories, in the weakly coupled limit trough a perturbative expansion in the coupling constant [25], or else in the infinite coupling limit for holographic fluids [1,20,26,27,28,29,30,31,32,33,34,35]. Since in this paper we shall only consider conformally invariant theories with no conserved charges, it is natural to restrict ourselves to the LandauLifshitz approach, to be discussed in more detail below These first generation FOTs were proven to violate causality and to have no stable solutions [40,41,42,43,44,45,46,47,48]. For completeness we present the relevant dispersion relations for ideal and Landau-Lifshitz fluids and causal FOTs [14] in Appendix A
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