Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

Abstract

We show that the Einstein-aether theory of Jacobson and Mattingly (J) can be understood in the framework of the metric-affine (gauge theory of) gravity (MAG). We achieve this by relating the aether vector field of J to certain post-Riemannian nonmetricity pieces contained in an independent linear connection of spacetime. Then, for the aether, a corresponding geometrical curvature-square Lagrangian with a massive piece can be formulated straightforwardly. We find an exact spherically symmetric solution of our model.