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Jack wrote in part:And, conversely, I would not have put it Joel's way, having
. . .
The static gravitational effects that we can observe are--------------------------------------snip----------------------------
embedded in the
metric (more strictly, the curvature) outside of the horizon. In the
usual metric, the gravitational effects get larger and larger as we
approach the black hole until they blow up at the horizon,
where there is
a coordinate singularity. . . .
There exist other coordinate systems to describe a Schwarzchild black hole
that have no coordinate singularities at the event horizon. One oft cited
example are the Kruskal-Szekeres coordinates (named after their creators, I
assume) See the book "Gravitation" by Misner, Thorne and Wheeler (know to
many students as MTW) around page 831 for a discussion.
Joel