# On the relativistic compressibility conditions

## TL;DR

This paper explores the constraints of relativistic compressibility on sound speed in fluids, deriving hydrodynamic conditions for perfect fluids and analyzing ideal gas models within a relativistic framework.

## Contribution

It introduces new relativistic compressibility conditions and applies them to ideal gases and Stephani models, expanding understanding of relativistic fluid dynamics.

## Key findings

- Derived constraints on sound speed in relativistic fluids.
- Established hydrodynamic conditions for perfect energy tensors.
- Analyzed the physical viability of ideal gas Stephani models.

## Abstract

The constraints imposed by the relativistic compressibility hypothesis on the square of the speed of sound in a medium are obtained. This result allows to obtain purely hydrodynamic conditions for the physical reality of a perfect energy tensor representing the energetic evolution of a perfect fluid in local thermal equilibrium. The results are applied to the paradigmatic case of the generic ideal gases. Then the physical reality of the ideal gas Stephani models is analyzed and the Rainich-like theory for ideal gas solutions is built.