On the electromagnetic field and the Teukolsky–Press relations in arbitrary space-times

Abstract

The relations on the electromagnetic field obtained by Teukolsky and Press for type D vacuum space-times are considered; these are four second-order equations in two complex components of the field with respect to a principal null tetrad. A rigorous geometric interpretation of these relations is given, showing the essential role played by the Maxwellian character of the basic null tetrad. It appears that, generically, the Teukolsky–Press relations are incomplete. Once completed, their generalizations to the general Maxwell equations (with source term) with respect to non-necessarily Maxwellian tetrads on arbitrary space-times are given.