  The theory of non-expanding horizons (NEH) geometry and the theory of near
horizon geometries (NHG) are two mathematical relativity frameworks
generalizing the black hole theory. From the point of view of the NEHs theory,
a NHG is just a very special case of a spacetime containing an NEH of many
extra symmetries. It can be obtained as the Horowitz limit of a neighborhood of
an arbitrary extremal Killing horizon. An unexpected relation between the two
of them, was discovered in the study of spacetimes foliated by a family of
NEHs. The class of 4-dimensional NHG solutions (either vacuum or coupled to a
Maxwell field) was found as a family of examples of spacetimes admitting a NEH
foliation. In the current paper we systematically investigate geometries of the
NEHs foliating a spacetime for arbitrary matter content and in arbitrary
spacetime dimension. We find that each horizon belonging to the foliation
satisfies a condition that may be interpreted as an invitation for a
transversal extremal Killing horizon to exist. Assuming the existence of a
transversal extremal Killing horizon, we derive all the spacetime metrics
satisfying the vacuum Einstein's equations.
