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