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.

arXiv comment20 pages, 8 figures; footnotes added, references changed

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• Universality Classes of Relativistic Fluid Dynamics: Foundations
• Branch-cut in the shear-stress response function of massless $\lambda {\phi }^4$ with Boltzmann statistics
• Universality Classes of Relativistic Fluid Dynamics: Applications
• Mean free path of photons in relativistic heavy ion collisions
• Field Theory Approaches to Relativistic Hydrodynamics
• Causal third-order viscous hydrodynamics within relaxation-time approximation
• The evolution equation for the energy-momentum moments of the non-equilibrium density function & The regularized relativistic third order hydrodynamics
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• Nonlinear analysis of causality for heat flow in heavy-ion collisions: constraints from equation of state