Stable First-order Particle-frame Relativistic Hydrodynamics for Dissipative Systems

Abstract

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.

4 pages, 3 figures

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• Second-order Relativistic Hydrodynamic Equations for Viscous Systems; how does the dissipation affect the internal energy?
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• In-flight dissipation as a mechanism to suppress Fermi acceleration
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• Transport coefficients of magnetized neutron star cores
• Bivelocity picture in the nonrelativistic limit of relativistic hydrodynamics
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• Jeans instability analysis in the presence of heat in Eckart's frame
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