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

TL;DR

This paper analyzes the phase space structure of Hořava-Lifshitz gravity, revealing issues with constraints and degrees of freedom that challenge its canonical formulation.

Contribution

It provides a detailed Hamiltonian analysis showing the lack of canonical structure and the reduction of degrees of freedom in Hořava-Lifshitz theory.

Findings

Poisson brackets do not form a closed algebra.

Many new constraints emerge from the analysis.

The phase space is reduced to no degrees of freedom or an odd number of fields.

Abstract

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.