Hamiltonian formulation of an effective modified gravity with nondynamical background fields

The current paper is dedicated to developing a (3+1) decomposition for the minimal gravitational Standard-Model Extension. Our setting explicit diffeomorphism violation and we focus on background fields known in literature as $u$ $s^{\mu\nu}$. Hamiltonian formalism developed these contributions, which amounts deriving modified momentum constraints. We then study connection between constraints Einstein equations. Implications are drawn form of guarantee internal consistency corresponding modified-gravity theories. In course our analysis, obtain set requirements certain sectors argue that constraint structure remains untouched when conditions satisfied. results shed light violations invariance local Lorentz gravity. They may turn out be valuable better understanding effective