Local thermal equilibrium and ideal gas Stephani universes

TL;DR

This paper classifies Stephani universes that can be interpreted as ideal gases in local thermal equilibrium, identifying classes of models and their physical behaviors, and noting the absence of exact classical ideal gas solutions.

Contribution

It provides a comprehensive classification of Stephani universes compatible with ideal gas thermodynamics, including regular and singular models, and explores their physical properties.

Findings

No exact classical ideal gas Stephani universe exists.

All models can approximate a classical ideal gas at first order in temperature.

Five classes of thermodynamic schemes lead to different model behaviors.

Abstract

The Stephani universes that can be interpreted as an ideal gas evolving in local thermal equilibrium are determined. Five classes of thermodynamic schemes are admissible, which give rise to five classes of regular models and three classes of singular models. No Stephani universes exist representing an exact solution to a classical ideal gas (one for which the internal energy is proportional to the temperature). But some Stephani universes may approximate a classical ideal gas at first order in the temperature: all of them are obtained. Finally, some features about the physical behavior of the models are pointed out.