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Nonlinear gravito-electromagnetism

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Abstract

There is a non-linear and covariant electromagnetic analogy for gravity, in which the full Bianchi identities are Maxwell-type equations for the free gravitational field, encoded in the Weyl tensor. This tensor gravito-electromagnetism is based on a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, and includes all non-linear effects from the gravitational field and matter sources. The non-linear vacuum Bianchi equations are invariant under spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. The super-energy density and super-Poynting vector of the gravitational field are natural duality invariants, and satisfy a super-energy conservation equation.

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  1. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG, UK

    Roy Maartens

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Maartens, R. Nonlinear gravito-electromagnetism. Gen Relativ Gravit 40, 1203–1217 (2008). https://doi.org/10.1007/s10714-007-0600-6

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