Linear plane waves in dissipative relativistic fluids

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Abstract
This paper analyzes the dispersion relations for linear plane waves in the Eckart and the Israel-Stewart theories of dissipative relativistic hydrodynamics. We show that in the long-wavelength (compared to a typical mean-free-path-length) limit the complicated dynamical structure of the Israel-Stewart theory reduces to the familiar dynamics of classical fluids: 9 of the 14 modes of an Israel-Stewart fluid are strongly damped in this limit, two propagate at the adiabatic sound speed (with appropriate viscous and thermal damping), two transverse shear modes decay at the classical viscous damping rate, and the final longitudinal mode is damped at the classical thermal diffusion rate. The short-wavelength limit of these dispersion relations is also examined. We demonstrate that the phase and group velocities of these waves must approach the characteristic velocities in the short-wavelength limit. Finally, we show how some of the perturbations of an Eckart fluid violate causality.

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