Thermodynamic Interpretation of the Kompanneets-Chernov-Kantowski-Sachs Solutions

TL;DR

This paper interprets certain homogeneous solutions in general relativity as thermodynamic fluids, analyzing their properties, conditions for physical realism, and solutions for ideal gases and relativistic gamma-law models.

Contribution

It provides a thermodynamic interpretation of Kompanneets-Chernov-Kantowski-Sachs solutions and explores their behavior as ideal gases within a relativistic framework.

Findings

Macroscopic conditions for physical reality are satisfied in wide spacetime regions.

Field equations for a classical ideal gas are derived.

Solutions for specific relativistic gamma-law cases are obtained.

Abstract

The spatially homogeneous perfect fluid solutions by Kompanneets-Chernov-Kantowski-Sachs are interpreted as a thermodynamic perfect fluid in isentropic evolution, namely, the isentropic limit of their non-homogeneous generalizations, the T-models. Some specific solutions that model a generic ideal gas are examined, and the associated thermodynamic variables are obtained. We show that the necessary macroscopic conditions for physical reality are fulfilled in wide spacetime domains. The field equations for a classical ideal gas are established, and the behavior of the solution is analyzed. The models fulfilling a relativistic $\gamma$-law are also examined, and the solutions for some particular cases are obtained.