  We consider a test, non-null electromagnetic field special in the sense that
the principal null directions of the field lie along the two repeated principal
null directions of the type D vacuum background. We prove that the special
non-null field is a valid solution of the Maxwell equations on a type D
background. This field behaves as $1/r^2$ and the only non-vanishing Maxwell
scalar is $\phi_1$ so it can be called the Coulomb field. We show that the
contribution to the energy and angular momentum fluxes of the Coulomb field
vanishes at any surface of integration, on the type D vacuum backgrounds Kerr,
Kerr-Taub-NUT, Taub-NUT, and Schwarzschild. Therefore this field does not lead
to any perturbations of the mass and angular momentum parameters of these
space-times.
