  For a vacuum initial data set of the Einstein field equations it is possible
to carry out a conformal rescaling or conformal compactification of the data
giving rise to an initial data set for the Friedrich vacuum conformal
equations. When will the data development with respect to the conformal
equations of this set be a conformal extension of a type D solution? In this
work we provide a set of necessary and sufficient conditions on a set of
initial data for the conformal equations that guarantees that the data
development of the conformal equations has a subset that is conformal to a
vacuum type D solution of the Einstein's equations. In particular we find the
conditions under which this vacuum solution corresponds to the Kerr solution.
Using our results we are able to show that there are no obstructions to extend
the Petrov type of the physical spacetime to the unphysical spacetime if the
conformal data are hyperboloidal.
