Thermodynamics of the Stephani Universes

TL;DR

This paper investigates the thermodynamic properties of Stephani Universes, a class of conformally flat cosmological solutions, revealing conditions for integrability and exploring the physical plausibility of their thermodynamic behavior.

Contribution

It provides explicit thermodynamic relations for Stephani Universes and analyzes the conditions under which these relations are consistent and physically meaningful.

Findings

Gibbs-Duhem relation is always integrable for certain symmetry groups.

Explicit forms of state variables and equations of state are derived.

Unphysical temperature evolution occurs if the free parameter is identified with FRW scale factor.

Abstract

We examine the consistency of the thermodynamics of the most general class of conformally flat solution with an irrotational perfect fluid source (the Stephani Universes). For the case when the isometry group has dimension $r\ge2$, the Gibbs-Duhem relation is always integrable, but if $r<2$ it is only integrable for the particular subclass (containing FRW cosmologies) characterized by $r=1$ and by admitting a conformal motion parallel to the 4-velocity. We provide explicit forms of the state variables and equations of state linking them. These formal thermodynamic relations are determined up to an arbitrary function of time which reduces to the FRW scale factor in the FRW limit of the solutions. We show that a formal identification of this free parameter with a FRW scale factor determined by FRW dynamics leads to an unphysical temperature evolution law. If this parameter is not identified with a FRW scale factor, it is possible to find examples of solutions and formal equations of state complying with suitable energy conditions and reasonable asymptotic behavior and temperature laws.