  The Noether charge method for defining the Hamiltonian of a
diffeomorphism-invariant field theory is applied to "Einstein-aether" theory,
in which gravity couples to a dynamical, timelike, unit-norm vector field.
Using the method, expressions are obtained for the total energy, momentum, and
angular momentum of an Einstein-aether space-time. The method is also used to
discuss the mechanics of Einstein-aether black holes. The derivation of Wald,
and Iyer and Wald, of the first law of black hole thermodynamics fails for this
theory, because the unit vector is necessarily singular at the bifurcation
surface of the Killing horizon. A general identity relating variations of
energy and angular momentum to a surface integral at the horizon is obtained,
but a thermodynamic interpretation, including a definitive expression for the
black hole entropy, is not found.
