  The Blandford-Znajek monopole is a conjectured solution of force-free
electrodynamics in the vicinity of a slowly rotating Kerr black hole,
supposedly defined as a perturbation in small angular momentum. It is used to
argue for the extraction of energy from rotating black holes by the
Blandford-Znajek process. We set up a careful analysis of the perturbative
definition of the Blandford-Znajek monopole, showing in particular that the
regime in which it is defined allows to use the technique of matched asymptotic
expansions. Our conclusion is that the Blandford-Znajek monopole, as it is
defined, is not consistent with demanding physically reasonable boundary
conditions far away from the event horizon. This puts into question the
existence of the Blandford-Znajek monopole, at least in the limit of slow
rotation of the Kerr black hole.
