Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: causality and stability

We investigate the causality and stability of three different relativistic dissipative fluid-dynamical formulations emerging from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. For this particular interaction, all transport coefficients of Navier...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Caio V P de Brito, Rocha, Gabriel S, Denicol, Gabriel S
Format: Article
Language:English
Subjects:
Dynamic stability
Fluid flow
Matching
Mathematical analysis
Navier-Stokes equations
Relativistic effects
Relativistic particles
Transport properties
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Summary:We investigate the causality and stability of three different relativistic dissipative fluid-dynamical formulations emerging from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. For this particular interaction, all transport coefficients of Navier-Stokes, Bemfica-Disconzi-Noronha-Kovtun and second-order transient theories can be computed in analytical form. We first show that Navier-Stokes theory is acausal and unstable regardless of the matching conditions. On the other hand, BDNK theory can be linearly causal and stable for a particular set of matching choices that does not contain the so-called exotic Eckart prescription. In particular, using the Liénard-Chipart criterion, we obtain a set of sufficient conditions that guarantee the stability of the theory. Last, second-order transient hydrodynamic theory in Landau matching is shown to be linearly causal and stable.
ISSN:2331-8422