Abstract
We consider spacetimes which in addition to admitting an isolated horizon also admit Killing horizons with or without an event horizon. We show that an isolated horizon is a Killing horizon provided either (1) it admits a stationary neighbourhood, or (2) it admits a neighbourhood with two independent, commuting Killing vectors. A Killing horizon is always an isolated horizon. For the case when an event horizon is definable, all conceivable relative locations of isolated horizon and event horizons are possible. The corresponding conditions are given.
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