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

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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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          Gravitational phenomenology in higher-dimensional theories and strings

          Stuart Samuel, V. Alan Kostelecký (1989)
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            Gravity with a dynamical preferred frame

            David Mattingly, Ted Jacobson (2000)
            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.
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              Gravity, Lorentz Violation, and the Standard Model

              Alan Kostelecky (2003)
              The role of the gravitational sector in the Lorentz- and CPT-violating Standard-Model Extension (SME) is studied. A framework is developed for addressing this topic in the context of Riemann-Cartan spacetimes, which include as limiting cases the usual Riemann and Minkowski geometries. The methodology is first illustrated in the context of the QED extension in a Riemann-Cartan background. The full SME in this background is then considered, and the leading-order terms in the SME action involving operators of mass dimension three and four are constructed. The incorporation of arbitrary Lorentz and CPT violation into general relativity and other theories of gravity based on Riemann-Cartan geometries is discussed. The dominant terms in the effective low-energy action for the gravitational sector are provided, thereby completing the formulation of the leading-order terms in the SME with gravity. Explicit Lorentz symmetry breaking is found to be incompatible with generic Riemann-Cartan geometries, but spontaneous Lorentz breaking evades this difficulty.
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                Author and article information

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                Publication date Created: 01 April 2005
                Article
                DOI: 10.1103/PhysRevD.72.025012
                ArXiV ID: gr-qc/0504005
                SO-VID: 649f9926-0158-4caa-83a1-17109742050c
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                Journal reference Phys.Rev.D72:025012,2005
                Comments Revtex4, 38 pages, 1 figure
                Categories gr-qc hep-th

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