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

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...

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Hauptverfasser: Schatz, Konrad, von Borzeszkowski, Horst-Heino, Chrobok, Thoralf
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Sprache:eng
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Zusammenfassung: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.
DOI:10.48550/arxiv.1412.0128