  The Hamiltonian formulation of the gravitational sector of the Standard-Model
Extension (SME) with nondynamical fields $u$ and $s^{\mu \nu}$ is studied. We
provide the relevant Hamiltonians that describe the constrained phase space and
the dynamics of the induced metric on the ADM hypersurface. The generalization
of the Gibbons-Hawking-York boundary term has been crucial to preventing second
time-derivatives of the metric tensor in the Hamiltonians. By extracting the
dynamics and constraints from the Einstein equations we have proved the
equivalence between the Lagrangian and Hamiltonian formulations.
