  The horizon and geodesic structure of static configurations generated by
anisotropic conformal transforms of the Schwarzschild metric is analyzed. We
construct the maximal analytic extension of such off--diagonal vacuum metrics
and conclude that for small deformations there are different classes of vacuum
solutions of the Einstein equations describing "black ellipsoid" objects. This
is possible because, in general, for off--diagonal metrics with deformed
non--spherical symmetries and associated anholonomic frames the conditions of
the uniqueness black hole theorems do not hold.
