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

Christian Heinicke·Peter Baekler·Friedrich W. Hehl
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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.

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Christian Heinicke, Peter Baekler, Friedrich W. Hehl. 2005-04-01. Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity. https://doi.org/10.1103/physrevd.72.025012

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