Republication of: A threedimensional formulation of the Bianchi identities for vacuum gravitational fields.

This paper was first published as Chapter III of the third part of a three-part final report under Contract AF 61(052)-567 at the University of Hamburg, which was funded by the US Air Force and entitled Contributions to Actual Problems of General Relativity. The work can be considered an addition to the 'Hamburg Bible' series published between 1960–1962 in the Proceedings of the Academy of Sciences and Literature in Mainz (Germany), and included earlier in this Golden Oldies series. It has been cited in later papers as a preprint or 'unpublished'. It presents for the first time the form of the Bianchi identities in terms of the electric and magnetic parts of the Weyl tensor in a 3+1 formalism. Their close analogy with Maxwell's equations of electromagnetism, including a division into constraint and propagation equations, has been influential, as has the wider focus on the electric/magnetic split. In the present paper the Bianchi identities are used in analyses of the purely electric and purely magnetic cases. [ABSTRACT FROM AUTHOR]