Onshell Lagrangian of an ideal gas
Abstract
In the context of general relativity, both energy and linearmomentum constraints lead to the same equation for the evolution of the speed of free localized particles with fixed proper mass and structure in a homogeneous and isotropic FriedmannLemaîtreRobertsonWalker universe. In this paper we extend this result by considering the dynamics of particles and fluids in the context of theories of gravity nonminimally coupled to matter. We show that the equation for the evolution of the linear momentum of the particles may be obtained irrespective of any prior assumptions regarding the form of the onshell Lagrangian of the matter fields. We also find that consistency between the evolution of the energy and linear momentum of the particles requires that their volumeaveraged onshell Lagrangian and energymomentum tensor trace coincide (L_{on shell}=T ). We further demonstrate that the same applies to an ideal gas composed of many such particles. This result implies that the two most common assumptions in the literature for the onshell Lagrangian of a perfect fluid (L_{on shell}=P and L_{on shell}=ρ , where ρ and P are the proper density and pressure of the fluid, respectively) do not apply to an ideal gas, except in the case of dust (in which case T =ρ ).
 Publication:

Physical Review D
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevD.105.104005
 arXiv:
 arXiv:2203.04022
 Bibcode:
 2022PhRvD.105j4005A
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 8 pages, no figures