Action functionals for relativistic perfect fluids

TL;DR

This paper develops various action functionals for relativistic perfect fluids, including their Hamiltonian forms, symmetries, and boundary conditions, enhancing the theoretical framework for modeling such fluids in relativistic contexts.

Contribution

It introduces new action functionals for relativistic perfect fluids with different equations of state and analyzes their Hamiltonian structures and symmetries.

Findings

Derived canonical Hamiltonian forms of the actions

Identified symmetries and conserved charges

Discussed boundary and initial value problems

Abstract

Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered here depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.