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

TL;DR

This paper demonstrates that Einstein-aether theory can be integrated into metric-affine gravity by relating the aether vector to nonmetricity, leading to new solutions including an exact spherically symmetric one.

Contribution

It establishes a connection between Einstein-aether theory and metric-affine gravity, introducing a geometrical curvature-square Lagrangian with a massive component.

Findings

Relation of aether vector to nonmetricity in MAG

Formulation of a curvature-square Lagrangian for aether

Derivation of an exact spherically symmetric solution

Abstract

We show that the Einstein-aether theory of Jacobson and Mattingly (J&M) 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&M 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.