Flux-variational formulation of relativistic perfect fluids

Action functionals for relativistic perfect fluids

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. Parti...

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 these actions, S, the fluid four–velocity is expressed as a sum of products of scalar fields and their gradients (the velocity–potential representation). For the other action, S̄, the fluid four–velocity is proportional to the totally antisymmetric product of ...

The Hamiltonian Structure of General Relativistic Perfect Fluids

We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift,, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evol...

Variational Formulation of Problems and Variational Methods

Solution generating with perfect fluids

We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect-fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a “seed” solution of the Einstein-perfect-fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of stat...