Action functionals for relativistic perfect fluids

Abstract

Action functionals describing relativistic perfect fluids are presented. Two\nof these actions apply to fluids whose equations of state are specified by\ngiving the fluid energy density as a function of particle number density and\nentropy per particle. Other actions apply to fluids whose equations of state\nare specified in terms of other choices of dependent and independent fluid\nvariables. Particular cases include actions for isentropic fluids and\npressureless dust. The canonical Hamiltonian forms of these actions are\nderived, symmetries and conserved charges are identified, and the boundary\nvalue and initial value problems are discussed. As in previous works on perfect\nfluid actions, the action functionals considered here depend on certain\nLagrange multipliers and Lagrangian coordinate fields. Particular attention is\npaid to the interpretations of these variables and to their relationships to\nthe physical properties of the fluid.\n