Nonlinear gravito-electromagnetism

Roy Maartens*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1203-1217
JournalGeneral Relativity and Gravitation
Issue number6
Publication statusPublished - Jun 2008


  • Electromagnetism
  • General relativity


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