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Killing spinors and massless spinor fields

It is shown that in a space–time that admits a Killing spinor any solution of the Weyl or of the Maxwell equations can be used as a potential for another solution of the corresponding equation. Furthermore, it is shown that the new solution can be generated by a single component of the given one, which satisfies a decoupled equation. For the Kerr metric, the connection between the procedure presented here and several results previously known is established.