Approximation to the Second Order Approximation of Einstein Field Equations with a Cosmological Constant in a Flat Background
Abstract
Einstein field equations with a cosmological constant are approximated to the second order in the perturbation to a flat background metric. The final result is a set of Einstein-Maxwell-Proca equations for gravity in the weak field regime. This approximation procedure implements the breaking of gauge symmetry in general relativity. A brief discussion of the physical consequences (Pioneer anomalous deceleration) is proposed in the framework of the gauge theory of gravity.
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