The separability of Maxwell’s equations in type-D backgrounds

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Abstract
It is shown that in a type-D space-time that admits a two-index Killing spinor a differential operator can be constructed that maps a solution of the Maxwell equations into another solution. By considering as a background the Plebański–Demiański metric, which includes all the vacuum type-D metrics, this operator is used to obtain all the components of the electromagnetic field and the vector potential. The separated functions appearing in the solutions are shown to obey identities of the Teukolsky–Starobinsky type and the separable solutions are shown to be eigensolutions of a certain differential operator with the ‘‘Starobinsky constant’’ as the eigenvalue.

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