Abstract
The Hamiltonian formulation of Hořava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second class, except for a global, first-class part that generates time reparametrizations. A reduced phase space formulation is given in which the local part of the scalar constraint is solved formally for the lapse as a function of the 3 metric and its conjugate momentum. In the infrared limit the scalar constraint is linear in the square root of the lapse. For asymptotically flat boundary conditions the Hamiltonian is a sum of bulk constraints plus a boundary term that gives the total energy. This energy expression is identical to the one for Einstein-aether theory which, for static spherically symmetric solutions, is the usual Arnowitt-Deser-Misner energy of general relativity with a rescaled Newton constant.
- Received 1 July 2011
DOI:https://doi.org/10.1103/PhysRevD.84.104019
© 2011 American Physical Society