Non-perturbative analysis of the gravitational energy in Ho\v{r}ava Theory

TL;DR

This paper conducts a non-perturbative analysis of Hořava gravity's constraints, deriving explicit gravitational energy expressions, and discusses reformulating the theory to involve only first class constraints, with implications for its quantum formulation.

Contribution

It provides a non-perturbative solution to the constraints of Hořava gravity and explores reformulating the theory using a master action with only first class constraints.

Findings

Gravitational energy in Hořava theory is explicitly derived and shown to be positive under certain conditions.

The theory's constraints include both first and second class, affecting its quantization.

The Minkowski metric minimizes the energy in the theory.

Abstract

We perform a non-perturbative analysis of the constraints of the Ho\v{r}ava Gravitational theory. In distinction to Einstein gravity the theory has constraints of the first class together with second class ones. We analyze the consequences of having to impose second classes constraints at any time in the quantum formulation of the theory. The second class constraints are formulated as strongly elliptic partial differential equations allowing a global analysis on the existence and uniqueness of the solution. We discuss the possibility of formulating the theory in terms of a master action with first class constraints only. In this case the Ho\v{r}ava theory would correspond to a gauged fixed version of the master theory. Finally we obtain, using the non-perturbative solution of the constraints, the explicit expression of the gravitational energy. It is, under some assumptions, always positive and the solution of Ho\v{r}ava field equations at minimal energy is the Minkowski metric.