The ADM Formulation of SME Gravity

The Hamiltonian formulation of the gravitational sector of the Standard-Model Extension with nondynamical fields u and s^μν 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 prevent 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.