A Trouble with Ho\v{r}ava-Lifshitz Gravity

Understand

We study the structure of the phase space in Ho\v{r}ava-Lifshitz theory.

• With the constraints derived from the action, the phase space is described by five fields, thus there is a lack of canonical structure.
• The Poisson brackets of the Hamiltonian density do not form a closed structure, resulting in many new constraints.
• Taking these new constraints into account, it appears that there is no degree of freedom left, or the phase space is reduced to one with an odd number of fields.