Note About Hamiltonian Formalism of Healthy Extended Horava-Lifshitz Gravity

Abstract: In this paper we continue the study of the Hamiltonian formalism of the healthy extended Horava-Lifshitz gravity. We find the constraint structure of given theory and argue that this is the theory with the second class constraints. Then we discuss physical consequence of this result. We also apply the Batalin-Tyutin formalism of the conversion of the system with the second class constraints to the system with the first class constraints to the case of the healthy extended Horava-Lifshitz theory. As a result we find new theory of gravity with structure that is different from the standard formulation of Horava-Lifshitz gravity or General Relativity.