Non-perfect-fluid space-times in thermodynamic equilibrium and generalized Friedmann equations

TL;DR

This paper derives the energy-momentum tensor for non-perfect fluids in thermodynamic equilibrium within conform-stationary, homogeneous space-times, leading to generalized Friedmann equations and encompassing various classical models.

Contribution

It provides a closed-form formulation of energy density, pressure, and heat flux for non-perfect fluids without assuming specific thermodynamic equations of state.

Findings

Generalized Friedmann equations derived for non-perfect fluids.

Recovery of Friedmann, G"odel, and Bianchi models as special cases.

Extension to rotating, dissipative fluid models in cosmology.

Abstract

We determine the energy-momentum tensor of non-perfect fluids in thermodynamic equilibrium. To this end, we derive the constitutive equations for energy density, isotropic and anisotropic pressure as well as for heat-flux from the corresponding propagation equations and by drawing on Einstein's equations. Following Obukhov at this, we assume the corresponding space-times to be conform-stationary and homogeneous. This procedure provides these quantities in closed form, i.e., 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 G\"odel models as well as non-tilted 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.