The Hamiltonian Structure of General Relativistic Perfect Fluids
نویسندگان
چکیده
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 evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed.
منابع مشابه
On Relativistic Material Reference Systems
This work closes certain gaps in the literature on material reference systems in general relativity. It is shown that perfect fluids are a special case of DeWitt’s relativistic elastic media and that the velocity–potential formalism for perfect fluids can be interpreted as describing a perfect fluid coupled to a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is carried...
متن کاملThe Rest - Frame Instant Form of Relativistic Perfect Fluids with Equation of State ρ = ρ ( n , s ) and of Non - Dissipative Elastic Materials
For perfect fluids with equation of state ρ = ρ(n, s), Brown [1] gave an action principle depending only on their Lagrange coordinates αi(x) without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for t...
متن کاملGeneralized Eulerian Coordinates for Relativistic Fluids: Hamiltonian Rest-Frame Instant Form, Relative Variables, Rotational Kinematics
We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on the Wigner hyper-planes, we define orientational and shape variables for the fluid, viewed as a relativistic extended deformable body, by introducing dynamic...
متن کاملAction 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...
متن کاملEulerian Coordinates for Relativistic Fluids: Hamiltonian Rest-Frame Instant Form, Relative Variables, Rotational Kinematics
We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of Eulerian coordinates. After the separation of the relativistic center of mass from the relative variables on the Wigner hyperplanes, we define orientational and shape variables for the fluid, viewed as a relativistic extended deformable body, by introducing dynamical body frames. Finally we defi...
متن کامل