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Closed 3-forms in Ricci-flat spacetimes

S Bonanos

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LETTER TO THE EDITOR

Using certain algebraic and differential identities satisfied by the Weyl curvature spinor in an algebraically general vacuum spacetime, we construct new 3-forms, quadratic in the connection, that can be expressed as exterior derivatives of corresponding 2-forms, in the same way as the Sparling 3-form is the exterior derivative of the Nester - Witten 2-form. These 3-forms thus imply the existence of new conserved pseudotensors in such spacetimes.


PACS

04.20.Cv Fundamental problems and general formalism

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

83C60 Spinor and twistor methods; Newman-Penrose formalism

Subjects

Gravitation and cosmology

Dates

Issue 5 (May 1997)

Received 10 February 1997



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