Hamiltonian Theory of a Relativistic Perfect Fluid

The velocity-potential version of the hydrodynamics of a relativistic perfect fluid is put into Hamiltonian form by applying Dirac's method to the version's degenerate Lagrangian. There is only one independent momentum, and the Hamiltonian density is $-T_0^{}{}_{}{}^0{(-g^{00})}^{-\frac{1}{2}}$. The Einstein equations for a perfect fluid are then put into Hamiltonian form by analog with Arnowitt, Deser, and Misner's vacuum Einstein equations. The Hamiltonian density splits into two pieces, which are the coordinate densities of energy and momentum of the fluid relative to an observer at rest on the hypersurface of constant coordinate time.