Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

Abstract

We determine the energy-momentum tensor of nonperfect fluids in thermodynamic equilibrium and, respectively, near to it. To this end, we derive the constitutive equations for energy density and isotropic and anisotropic pressure as well as for heat-flux from the corresponding propagation equations and by drawing on Einstein’s equations. Following Obukhov on this, we assume the corresponding space-times to be conform-stationary and homogeneous. This procedure provides these quantities in closed form, that is, in terms of the structure constants of the three-dimensional isometry group of homogeneity and, respectively, in terms of the kinematical quantities expansion, rotation, and acceleration. In particular, we find a generalized form of the Friedmann equations. As special cases we recover Friedmann and Gödel models as well as nontilted Bianchi solutions with anisotropic pressure. All of our results are derived without assuming any equations of state or other specific thermodynamic conditions a priori. For the considered models, results in literature are generalized to rotating fluids with dissipative fluxes.