Gravito-electromagnetism

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Abstract
We develop and apply a fully covariant 1+3 electromagnetic analogy forgravity. The free gravitational field is covariantly characterized by the Weylgravito-electric and gravito-magnetic spatial tensor fields, whose dynamicalequations are the Bianchi identities. Using a covariant generalization ofspatial vector algebra and calculus to spatial tensor fields, we exhibit thecovariant analogy between the tensor Bianchi equations and the vector Maxwellequations. We identify gravitational source terms, couplings and potentialswith and without electromagnetic analogues. The nonlinear vacuum Bianchiequations are shown to be invariant under covariant spatial duality rotation ofthe gravito-electric and gravito-magnetic tensor fields. We construct thesuper-energy density and super-Poynting vector of the gravitational field asnatural U(1) group invariants, and derive their super-energy conservationequation. A covariant approach to gravito-electric/magnetic monopoles is alsopresented.

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