Wave zone in the Ho\v{r}ava-Lifshitz theory at the kinetic-conformal point in the low energy regime

TL;DR

This paper demonstrates that in the Hořava-Lifshitz theory at the kinetic-conformal point, a consistent wave zone exists where physical gravitational waves propagate, aligning with General Relativity under certain conditions.

Contribution

It establishes the existence of a wave zone in the low energy regime of the Hořava-Lifshitz theory and derives the physical Hamiltonian and degrees of freedom in this context.

Findings

Physical degrees of freedom satisfy a linear wave equation.

Wave equation matches relativistic form for specific couplings.

Hamiltonian and degrees of freedom are explicitly characterized.

Abstract

We show that in the Ho\v{r}ava-Lifshitz theory at the kinetic-conformal point, in the low energy regime, a wave zone for asymptotically flat fields can be consistently defined. In it, the physical degrees of freedom, the transverse traceless tensorial modes, satisfy a linear wave equation. The Newtonian contributions, among which there are terms which manifestly break the relativistic invariance, are non-trivial but do not obstruct the free propagation (radiation) of the physical degrees of freedom. For an appropriate value of the couplings of the theory, the wave equation becomes the relativistic one in agreement with the propagation of the gravitational radiation in the wave zone of General Relativity. Previously to the wave zone analysis, and in general grounds, we obtain the physical Hamiltonian of the Ho\v{r}ava-Lifshitz theory at the kinetic-conformal point in the constrained submanifold. We determine the canonical physical degrees of freedom in a particular coordinate system. They are well defined fuctions of the transverse-traceless modes of the metric and coincide with them in the wave zone and also at linearized level.