Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics

Abstract

Within the FTBDNK family of formulations of relativistic Navier-Stokes (H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014), Proc. R. Soc. A 473 (2017), 20160729; F. S. Bemfica, M. Disconzi, and J. Noronha, Phys. Rev. D 98, 104064 (2018), Phys. Rev. D 100, 104020 (2019); P. Kovtun, J. High Energy Phys. 2019, 034 (2019)), this paper collects some consistency properties for certain causal hyperbolic five-field theories obtained from the Landau-Lifshitz formulation via Eulerian gradient shifts, a family, EGS(L), of models that slightly generalize a class identified in H. Freistühler, J. Math.\ Phys. 61, 033101 (2020). With $\epsilon$ the magnitude of the dissipation coefficients that quantify viscosity and heat conduction, the paper shows that any element of EGS(L) is $O({\epsilon }^2)$ equivalent to the Landau-Lifshitz formulation, has an $O({\epsilon }^3)$ excess entropy production, represents heterogeneous local thermodynamic equilibria cleanly, and admits regular heteroclinic profiles for all shock waves of sufficiently small amplitude.