# Thermodynamic class II Szekeres-Szafron solutions. Singular models

## TL;DR

This paper investigates a family of inhomogeneous thermodynamic solutions within class II Szekeres-Szafron models, analyzing their physical viability and interpretations under different thermodynamic schemes, including a new homogeneous temperature model.

## Contribution

It introduces and analyzes a new inhomogeneous thermodynamic model with a specific ideal gas behavior and compares three thermodynamic schemes within class II Szekeres-Szafron solutions.

## Key findings

- Models satisfy physical reality conditions in wide spacetime domains
- Three thermodynamic interpretations are thoroughly analyzed
- A new homogeneous temperature model consistent with FLRW limit is proposed

## Abstract

A family of parabolic Szekeres-Szafron class II solutions in local thermal equilibrium is studied and their associated thermodynamics are obtained. The subfamily with the hydrodynamic behavior of a generic ideal gas (defined by the equation of state $p = k n \Theta$) results to be an inhomogeneous generalization of flat FLRW $\gamma$-law models. Three significative interpretations that follow on from the choice of three specific thermodynamic schemes are analyzed in depth. First, the generic ideal gas in local thermal equilibrium; this interpretation leads to an inhomogeneous temperature $\Theta$. Second, the thermodynamics with homogeneous temperature considered by Lima and Tiomno (CQG 6 1989). And third, a new model having exactly the homogeneous temperature of the FLRW limit. It is shown that the three models above fulfill the necessary macroscopic requirements for physical reality (positivity of matter density and temperature, energy conditions and compressibility conditions) in wide domains of the spacetime.