  We consider $3$-dimensional isolated horizons (IHs) generated by null curves
that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH
geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov
type D equation introduced and studied in previous works
\cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view,
solutions to that equation define isolated horizons embeddable in vacuum
spacetimes (with cosmological constant) as Killing horizons to the second order
such that the spacetime Weyl tensor at the horizon is of the Petrov type D.
From the point of view of the $U(1)$-bundle structure, the equation couples a
$U(1)$-connection, a metric tensor defined on the base manifold and the surface
gravity in a very nontrivial way. We focus on the $U(1)$-bundles over
$2$-dimensional manifolds diffeomorphic to $2$-sphere. We have derived all the
axisymmetric solutions to the Petrov type D equation. For a fixed value of the
cosmological constant they set a $3$-dimensional family as one could expect. A
surprising result is, that generically our horizons are not embeddable in the
known exact solutions to Einstein's equations. It means that among the exact
type D spacetimes there exists a new family of spacetimes that generalize the
properties of the Kerr- (anti) de Sitter black holes on one hand and the
Taub-NUT spacetimes on the other hand.
