Relativistic dynamics of nonideal fluids: Viscous and heat-conducting fluids. I. General aspects and3+1formulation for nuclear collisions

Abstract

Relativistic nonideal fluid dynamics is formulated in $3+1$ space-time dimensions. The equations governing dissipative relativistic hydrodynamics are given in terms of the time and three-space quantities which correspond to those familiar from nonrelativistic physics. Dissipation is accounted for by applying the causal theory of relativistic dissipative fluid dynamics. As a special case, we consider a fluid without viscous/heat couplings in the causal system of transport/relaxation equations. For the study of physical systems, we consider pure ($1+1$)-dimensional expansion in planar geometry, ($1+1$)-dimensional spherically symmetric (fireball) expansion, ($1+1$)-dimensional cylindrically symmetric expansion, and a ($2+1$)-dimensional expansion with cylindrical symmetry in the transverse plane (firebarrel expansion). The transport/relaxation equations are given in terms of the spatial components of the dissipative fluxes, since these are not independent. The choice for the independent components is analogous to the nonrelativistic equations.