  The Hamiltonian formulation of Horava gravity is derived. In a closed
universe the Hamiltonian is a sum of generators of gauge symmetries, the
foliation-preserving diffeomorphisms, and vanishes on shell. The scalar
constraint is second class, except for a global, first-class part that
generates time reparametrizations. A reduced phase space formulation is given
in which the local part of the scalar constraint is solved formally for the
lapse as a function of the 3 metric and its conjugate momentum. In the infrared
limit the scalar constraint is linear in the square root of the lapse. For
asymptotically flat boundary conditions the Hamiltonian is a sum of bulk
constraints plus a boundary term that gives the total energy. This energy
expression is identical to the one for Einstein-aether theory which, for static
spherically symmetric solutions, is the usual Arnowitt-Deser-Misner energy of
general relativity with a rescaled Newton constant.

High Energy Physics - Theory;General Relativity and Quantum Cosmology