Diffeomorphism invariance and diffeomorphism generation in the Horava-Lifshitz gravity

Abstract

This paper is intended to study diffeomorphism invariance and diffeomorphism generation in the modified theory of gravity proposed by Horava. Firstly, we demonstrate that the theory does not lose diffeomorphism invariance due to the parameter $\lambda$, as it was previously believed. However, we show that the presence of terms containing the Levi-Civita symbol in the original proposal of Horava makes the theory diffeomorphism dependent. By neglecting such terms, what returns fully diffeomorphism invariance to the action, we obtain the equations of motion. Secondly, in the Hamiltonian formalism, we calculate the transformations generated by some of the constraints of the theory. Then, we prove that all diffeomorphisms of General Relativity are generated, on the energy shell, by the constraints of the Horava-Lifshitz gravity.