# Event Horizon = Singularity?

Is the event horizon of a blackhole (as seen by an observer at rest relative to the singularity) equivalent to the singularity (as seen by a free-falling observer)? In other words, if the stationary observer watches a rocketship free-fall to near the event horizon then turn on its rockets and return (much later), would the occupant of that rocket report that he saw no event horizon when he was free-falling but he did see himself approach close to the singularity? In other words, does space-time near the event-horizon in the stationary frame map to space-time near the singularity in the free-falling frame?

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