Hamiltonian formulation of the linearized hypersurface-orthogonal Einstein-aether theory

Abstract

We perform the Hamiltonian formulation of the Einstein-aether theory subject to the condition of hypersurface-orthogonality on the aether vector. Our main aim is to obtain the bulk Hamiltonian together with its constraints and their algebra. We implement a perturbative approach, studying the theory at the linearized level. Under the condition of hypersurface orthogonality the aether vector can be represented by a scalar field. The theory has two first-class constraints, which are associated to the symmetry of general diffeomorphisms over the spacetime. One of the constraints depends on the perturbative aether field, generating linear-order diffeomorphisms on it. We also present the reduced bulk Hamiltonian depending on the physical degrees of freedom. We find conditions on the coupling constants enusring the positiveness of the reduced Hamiltonian and the hyperbolicity of the propagation equations of the independent modes.