Relativistic viscoelastic fluid mechanics

Abstract

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

52pages, 11figures; v2: minor corrections; v3: minor corrections, to appear in Physical Review E; v4: minor changes

References in corpus (5)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• From Navier-Stokes To Einstein
• Stability and Causality in relativistic dissipative hydrodynamics
• Universal description of viscoelasticity with foliation preserving diffeomorphisms
• Entropic formulation of relativistic continuum mechanics

Cited by in corpus (11)

• Viscoelastic hydrodynamics and holography
• Effective action approach to cosmological perturbations in dark energy and modified gravity
• Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method
• Active viscoelasticity of odd materials
• Derivation of Hydrodynamics from the Hamiltonian description of particle systems
• How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
• Passive odd viscoelasticity
• Non-linear elasticity, yielding and entropy in amorphous solids
• Hydrodynamics of plastic deformations in electronic crystals
• Probe particles in odd active viscoelastic fluids: how activity and dissipation determine linear stability
• Entropic formulation of relativistic continuum mechanics