Einstein's quadrupole formula from the kinetic-conformal Horava theory

TL;DR

This paper demonstrates that the kinetic-conformal Horava gravity reproduces Einstein's quadrupole formula for gravitational radiation, sharing the same degrees of freedom as general relativity and showing no extra modes in the linearized regime.

Contribution

It shows that at the kinetic-conformal point, Horava gravity matches Einstein's quadrupole formula and has no additional radiative modes, aligning with general relativity in the linearized limit.

Findings

Only tensorial modes obey wave equations, others are nonradiative.

The quadrupole formula is recovered in the far zone for weak sources.

No monopole or dipole radiation modes are present.

Abstract

We analyze the radiative and nonradiative linearized variables in a gravity theory within the familiy of the nonprojectable Horava theories, the Horava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein's quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.