A new scalar-tensor realization of Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper introduces a covariant scalar-tensor model that realizes Hořava-Lifshitz gravity, featuring a new symmetry and spontaneous Lorentz symmetry breaking, resulting in a theory with a spin-two degree of freedom and solutions similar to General Relativity.

Contribution

It presents a novel covariant scalar-tensor realization of Hořava-Lifshitz gravity with a unique symmetry and no propagating scalar degrees of freedom in a specific gauge.

Findings

Existence of asymptotically flat, spherically symmetric solutions

Identification of solutions equivalent to those in General Relativity

Theory propagates a pure spin-two degree of freedom

Abstract

We discuss a new covariant scalar-tensor system aimed to realise Ho\v{r}ava proposal for a power-counting renormalizable theory of gravity, with the special feature of not propagating scalar degrees of freedom in an appropriate gauge. The theory is characterized by a new symmetry acting on the metric, that can protect the particular form of its interactions. The set-up spontaneously breaks Lorentz symmetry by means of a time-like scalar field profile. By selecting a unitary gauge for the scalar, we show that this theory describes the dynamics of a spin two degree of freedom, whose equations of motion contain two time derivatives and up to six spatial derivatives. We analytically determine asymptotically flat, spherically symmetric configurations, showing that there exists a branch of solutions physically equivalent to spherically symmetric configurations in General Relativity, also in the presence of matter fields.