Dust in the York Canonical Basis of ADM Tetrad Gravity: the Problem of
  Vorticity
  Brown's formulation of dynamical perfect fluids in Minkowski space-time is
extended to ADM tetrad gravity in globally hyperbolic, asymptotically
Minkowskian space-times. For the dust we get the Hamiltonian description in
closed form in the York canonical basis, where we can separate the inertial
gauge variables of the gravitational field in the non-Euclidean 3-spaces of
global non-inertial frames from the physical tidal ones. After writing the
Hamilton equations of the dust, we identify the sector of irrotational motions
and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces
of the non-inertial frame. The role of the inertial gauge variable York time
(the remnant of the clock synchronization gauge freedom) is emphasized. Finally
the Hamiltonian Post-Minkowskian linearization is studied. The future
application of this formalism will be the study of cosmological back-reaction
(as an alternative to dark energy) in the York canonical basis.
