On the linear causality and stability of third-order relativistic dissipative fluid dynamics

Abstract

We analyze the linear causality and stability of third-order fluid dynamics considering perturbations around a global equilibrium state. We investigate the formulation derived from kinetic theory, using the Chapman-Enskog expansion, in PRC 88, 021903, which was shown to be in excellent agreement with solutions of the microscopic theory. From this analysis, we demonstrate that this theory is linearly acausal and unstable and that such instabilities cannot be corrected by tuning the transport coefficients. We then propose a modification of this theory, valid only in the linear regime, that can be constructed to be linearly causal and stable and obtain the conditions the transport coefficients must satisfy in order for this to be the case.

20 pages, 8 figures; footnotes added, references changed

References in corpus (4)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Stability and Causality in relativistic dissipative hydrodynamics
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Relativistic third-order viscous corrections to the entropy four-current from kinetic theory

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