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.
Highlights
In this paper, we consider systems described by Einstein’s equations: Rab − Rgab = Tab (1)with an energy-momentum tensor and equations of state, neither of which are specified by any ad hoc assumptions
We determine the energy-momentum tensor of nonperfect fluids in thermodynamic equilibrium and, respectively, near to it
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
Summary
With an energy-momentum tensor and equations of state, neither of which are specified by any ad hoc assumptions. As shown in [21], regarding the conformal Killing equation (2), the second term in brackets turns out to be traceless which results in a vanishing entropy production σ (Tab − ρuaub − phab) (ξa;b + ξb;a) = 0 This shows that nonperfect fluids are not necessarily incompatible with reversible thermodynamics [28,29,30]. The CKV property is justified by defining equilibrium or near-equilibrium states in the framework of reversible thermodynamics [21] This is confirmed by the fact that ξa = ua/T, being a CKV, leads to some well-known models like Friedmann’s and Godel’s space-times with the corresponding equations of state (see Section 3.2).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
