Abstract
It is proved that if Fab=-Fba is a bivector field on Minkowskian space-time satisfying the wave equation, Square Operator Fab=0, and the derivatives of Fab satisfy certain smoothness and asymptotic conditions, then one can construct from Fab a bivector which satisfies Maxwell's vacuum field equations which, from another point of view, are equivalent to polarization conditions. The relationship between this result and the initial-value problem is solved by two different techniques. The extension of these results to the linearized Einstein field equations in vacuo is provided.
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