The extended Einstein–Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes

We study a generally covariant model in which local Lorentz invariance is broken "spontaneously" by a dynamical unit timelike vector field \(u^a\)---the "aether". Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative \(\nabla_{[a}u_{b]}\). Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.