Hamiltonian formulation of an effective modified gravity with nondynamical background fields

Understand

The current paper is dedicated to developing a (3+1) decomposition for the minimal gravitational Standard-Model Extension.

• Our setting is explicit diffeomorphism violation and we focus on the background fields known in the literature as $u$ and $s^{\mu\nu}$.
• The Hamiltonian formalism is developed for these contributions, which amounts to deriving modified Hamiltonian and momentum constraints.
• We then study the connection between these modified constraints and the modified Einstein equations.