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Originally Posted by Disinfo Agent
Listen carefully: space is not fully compacted at the event horizon. That only happens (if at all) at the singularity, which is beyond the horizon, inside the black hole. It's not at the event horizon that all the mass in the black hole is supposed to be compacted into infinite density, or that time is supposed to stop. All of that is supposed to happen at the singularity.
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From the distant observer these two are the same.
If time stops at the EH or if light can not escape then time has stopped. The light at exactly the EH would take an infinite time to reach us.
As one approaches a stop in time in order to keep the speed of light constant locally distances need to contract appropraitely. So as time slows ... the speed of light is constant so distances need to shorten. as we approach the stopage of time the space in that area needs to contract ( I am not sure if the dimensions curl up or what ) for example :
From wikipedia
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Today, it is defined by the International Bureau of Weights and Measures as the distance travelled by light in absolute vacuum in 1⁄299,792,458 of a second.
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so
m=c * 1⁄299,792,458 seconds
As seconds relatively shorten ( local observation vs distant observation ) then so must m. Removing the constants ...
m is proportial to t.
So if time is stopped the meter is a point. Or if you dont believe in that nonsense ... as time approaches stopping the meter approaches a point.
Now that all happens at the EH ( from the view point of a distant observer ).
So what is the sphere of the EH that you discuss ... At the point that a star collapses to the exact size of an EH the star no longer has any volume as any mesurements ( say in meters ) would make any sense since meters are a point ... per the above argument.
I think there is still a radius however but no volume. So the way I visualize this is a circle from any vantage point. However the circle is absolutely flat.