Gravitational waves in Ho\v{r}ava-Lifshitz anisotropic gravity

TL;DR

This paper demonstrates that in Hořava-Lifshitz gravity, gravitational waves propagate according to a non-relativistic high-order equation, reducing to the wave equation at low energies, with specific parameter restrictions ensuring finite energy.

Contribution

It provides a detailed analysis of gravitational wave propagation in Hořava-Lifshitz gravity beyond linear approximation, including high-order terms and energy considerations.

Findings

Existence of a well-defined wave zone in Hořava-Lifshitz gravity.

Propagation governed by a non-relativistic high-order equation.

Conditions on parameters for finite gravitational energy.

Abstract

We show that in the anisotropic Ho\v{r}ava-Lifshitz gravity there is a well-defined wave zone where the physical degrees of freedom propagate according to a non-relativistic linear evolution equation of high order in spatial derivatives, which reduces to the wave equation at low energy. This is so, provided the coupling parameters satisfy some restrictions which we study in detail. They are imposed to obtain a finite ADM gravitational energy, which depends manifestly on the terms which break the Lorentz symmetry of the formulation. The analysis we perform is beyond the linearized approach and includes all high order terms of the Hamiltonian potential.