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Symmetry 2018, 10(10), 490; https://doi.org/10.3390/sym10100490 (registering DOI)

Lorentz-Violating Gravity Models and the Linearized Limit

Department of Physics, Astronomy, and Geophysics, Connecticut College, New London, CT 06320, USA
Received: 7 September 2018 / Revised: 9 October 2018 / Accepted: 10 October 2018 / Published: 12 October 2018
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
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Abstract

Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “effective equation” for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any “tensor Klein–Gordon” model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects. View Full-Text
Keywords: Lorentz symmetry; linearized gravity; spontaneous symmetry breaking Lorentz symmetry; linearized gravity; spontaneous symmetry breaking
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Seifert, M. Lorentz-Violating Gravity Models and the Linearized Limit. Symmetry 2018, 10, 490.

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