Event Horizon = Singularity?

[Ray Eston Smith Jr]

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?

[pervect]

There's nothing particularly special about the event horizion as far as the geometry of space-time itself goes. Some coordinate systems (specifically, the typical Scwarzschild coordinates) are ill behaved there, but this is a property of the coordinates. The situation is roughly similar to using standard latitude and longitude coordiantes at the north pole of the earth - there is nothing special about the shape of the earth there, but a coordinate system based on lattitude and longitude goes a bit "wonky".