THE REST-FRAME INSTANT FORM OF RELATIVISTIC PERFECT FLUIDS WITH EQUATION OF STATE ρ=ρ(n, s) AND OF NONDISSIPATIVE ELASTIC MATERIALS

For perfect fluids with equation of state ρ=ρ(n, s), Brown¹ gave an action principle depending only on their Lagrange coordinates αⁱ(x) without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski space–time, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to nondissipative relativistic elastic materials described in terms of Lagrangian coordinates.