Abstract
The necessary and sufficient condition for a conservative perfect fluid energy tensor to be the energetic evolution of a classical ideal gas is obtained. This condition forces the square of the speed of sound to have the form in terms of the hydrodynamic quantities, energy density and pressure , being the (constant) adiabatic index. The inverse problem for this case is also solved, that is, the determination of all the fluids whose evolutions are represented by a conservative energy tensor endowed with the above expression of , and it shows that these fluids are, and only are, those fulfilling a Poisson law. The relativistic compressibility conditions for the classical ideal gases and the Poisson gases are analyzed in depth and the values for the adiabatic index for which the compressibility conditions hold in physically relevant ranges of the hydrodynamic quantities , are obtained. Some scenarios that model isothermal or isentropic evolutions of a classical ideal gas are revisited, and preliminary results are presented in applying our hydrodynamic approach to looking for perfect fluid solutions that model the evolution of a classical ideal gas or of a Poisson gas.
- Received 8 February 2019
DOI:https://doi.org/10.1103/PhysRevD.99.084035
© 2019 American Physical Society