Einstein-Aether Waves

TL;DR

This paper analyzes the wave modes in Einstein-Aether theory, a model where Lorentz invariance is broken by a dynamical vector field, revealing the speeds and polarizations of gravitational and aether-related waves.

Contribution

It provides a detailed linearized analysis of wave modes in Einstein-Aether theory, including their speeds and polarizations, based on the most general second-order action.

Findings

Identification of three coupled aether-metric wave modes

Determination of wave speeds and polarizations

Extension of gravitational wave analysis to Lorentz-violating theories

Abstract

Local Lorentz invariance violation can be realized by introducing extra tensor fields in the action that couple to matter. If the Lorentz violation is rotationally invariant in some frame, then it is characterized by an ``aether'', i.e. a unit timelike vector field. General covariance requires that the aether field be dynamical. In this paper we study the linearized theory of such an aether coupled to gravity and find the speeds and polarizations of all the wave modes in terms of the four constants appearing in the most general action at second order in derivatives. We find that in addition to the usual two transverse traceless metric modes, there are three coupled aether-metric modes.