LETTER TO THE EDITOR: Closed 3-forms in Ricci-flat spacetimes

Physics

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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.

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