Hamiltonian analysis of nonrelativistic covariant restricted-foliation-preserving diffeomorphism invariant Hořava-Lifshitz gravity

Abstract

We perform the Hamiltonian analysis of nonrelativistic covariant Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity in the formulation presented recently in arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in agreement with the original construction of nonrelativistic covariant Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this construction to the case of restricted-foliation-preserving diffeomorphism invariant Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory. We find a well behaved Hamiltonian system with the number of the first- and the second-class constraints that ensure the correct number of physical degrees of freedom of gravity.