ON VARIATIONAL-PRINCIPLES FOR GRAVITATING PERFECT FLUIDS

The connection is established between two different action principles for perfect fluids in the context of general relativity. For one of th ese actions, S, the fluid four-velocity is expressed as a sum of produ cts of scalar fields and their gradients (the Velocity-potential repre sentation). For the other action, (S) over bar, the fluid four-velocit y is proportional to the totally antisymmetric product of gradients of the fluid Lagrangian coordinates. The relationship between S and (S) over bar is established by expressing S in Hamiltonian form and identi fying certain canonical coordinates as ignorable. Elimination of these coordinates and their conjugates yields the action (S) over bar. The key step in the analysis is a point canonical transformation in which all tensor fields on space are expressed in terms of the Lagrangian co ordinate system supplied by the fluid. The canonical transformation is of interest in its own right. Tt can be applied to any physical syste m that includes a material medium described by Lagrangian coordinates. The result is a Hamiltonian description of the system in which the mo mentum constraint is trivial. (C) 1996 Academic Press. Inc.