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Posted by Bruce on January 2, 2001 03:51:00 UTC

the far away observers perspective.

Its just the perspective of the far away observer. The far away observer reckons the distance to the event horizon to be infinite.

drshell=dr/(1-2M/r)1/2
Substitute 2M for r.

It can be shown using the integral of the drshell expression
that the actual distance is finite. The far away observers perspective is unique because of the way the far away observer receives news (or
doesn't get the news) of the event.

The expression for dr/dt you derived from the metric is the far away observers perspective for the radial speed of light. The pulse of light appears to never get to the event horizon because light can't cross an infinite distance in a finite amount of time. Actually all news of the approaching event is gravitationally redshifted out of existence from the far away observers perspective.
But the local shell observer uses the metric for special relativity to measure the local radial speed of light.
dt2 = dt2shell-dr2shell-0 (the tangential term)
0=dt2shell-ds2shell
dsshell/dtshell = |1|
Speed expressed as v/c = 1
v=c

The far away observers perspective close to the black hole is really strange. Kip Thorne called it an optical illusion in 'Black Holes & Time Warps'

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