  With a help of a generalized Raychaudhuri equation non-expanding null
surfaces are studied in arbitrarily dimensional case. The definition and basic
properties of non-expanding and isolated horizons known in the literature in
the 4 and 3 dimensional cases are generalized. A local description of horizon's
geometry is provided. The Zeroth Law of black hole thermodynamics is derived.
The constraints have a similar structure to that of the 4 dimensional spacetime
case. The geometry of a vacuum isolated horizon is determined by the induced
metric and the rotation 1-form potential, local generalizations of the area and
the angular momentum typically used in the stationary black hole solutions
case.
