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What's going on is that you have to look at
the entire universe,
not just the black hole (something like donuts).
The Schwarzchild
geometry is the geometry of a universe with a large
mass at the center.
The static gravitational effects that we can observe
are 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. So the answer is that the
mass at the center
of the black hole has distorted all of space; part
of that distortion is
the event horizon that bounds the black hole.
Regards,
Jack