  We characterize a general solution to the vacuum Einstein equations which
admits isolated horizons. We show it is a non-linear superposition -- in
precise sense -- of the Schwarzschild metric with a certain free data set
propagating tangentially to the horizon. This proves Ashtekar's conjecture
about the structure of spacetime near the isolated horizon. The same
superposition method applied to the Kerr metric gives another class of vacuum
solutions admitting isolated horizons. More generally, a vacuum spacetime
admitting any null, non expanding, shear free surface is characterized. The
results are applied to show that, generically, the non-rotating isolated
horizon does not admit a Killing vector field and a spacetime is not
spherically symmetric near a symmetric horizon.
