  We introduce a Hamiltonian framework tailored to degrees of freedom (DOF) of
field theories that reside in suitable 3-dimensional open regions, and then
apply it to the gravitational DOF of general relativity. Specifically, these
DOF now refer to open regions of null infinity, and of black hole (and
cosmological) horizons representing equilibrium situations. At null infinity
the new Hamiltonian framework yields the well-known BMS fluxes and charges. By
contrast, all fluxes vanish identically at black hole (and cosmological)
horizons just as one would physically expect. In a companion paper we showed
that, somewhat surprisingly, the geometry and symmetries of these two physical
configurations descend from a common framework. This paper reinforces that
theme: Very different physics emerges in the two cases from a common
Hamiltonian framework because of the difference in the nature of degrees of
freedom. Finally, we compare and contrast this Hamiltonian approach with those
available in the literature.
